Due to the advances in location-acquisition techniques, citizen geospatial data has emerged with opportunity for research, development, innovation, and business. A variety of research has been developed to study society and citizens through exploring patterns from geospatial data. In this thesis, we investigate patterns of population and human sentiments using GPS trajectory data and geo-tagged tweets. Kernel density estimation and emerging hot spot analysis are first used to demonstrate population distribution across space and time. Then a flow extraction model is proposed based on density difference for human movement detection and visualization. Case studies with volleyball game in West Lafayette and traffics in Puerto Rico verify the effectiveness of this method. Flow maps are capable of tracking clustering behaviors and direction maps drawn upon the orientation of vectors can precisely identify location of events. This thesis also analyzes patterns of human sentiments. Polarity of tweets is represented by a numeric value based on linguistics rules. Sentiments of four US college cities are analyzed according to its distribution on citizen, time, and space. The research result suggests that social media can be used to understand patterns of public sentiment and well-being.

Cette thèse, portant sur le choix de localisation résidentielle des ménages, s’inscrit dans le cadre théorique de la microéconomie urbaine et de l’utilité aléatoire. Si l’approche des choix discrets reste la plus appropriée dans ce domaine, la difficulté réside dans l’adaptation de ce type de modèles au contexte spatial (autocorrélation spatiale, grand nombre d’alternatives de choix) d’une part, et dans la manière de définir l’échelle de désagrégation d’autre part. Pour ce faire, nous avons procédé en deux temps. Nous avons estimé un logit multinomial avec un échantillon aléatoire d’alternatives pour comprendre le processus de choix de localisation résidentielle, avant de tester l’apport d’une structure hiérarchique pour traiter les problèmes d’autocorrélation spatiale. Cela a aussi permis l’investigation d’une nouvelle méthode de correction des biais liés à l’échantillonnage d’alternatives dans le cas du modèle logit emboîté. En termes de résultats, nous avons montré que la qualité de l’environnement social est le facteur le plus déterminant, sans remettre en cause le poids toujours important de l’accessibilité à l’emploi. Au plan méthodologique, nous avons été en mesure de tester l’apport de l’utilisation d’un modèle logit emboîté pour analyser les choix de localisation de l’aire urbaine de Lyon. Cependant, nous n’avons pas pu dépasser la difficulté de séparer l’autocorrélation spatiale et entre les nids. Le calage du modèle de choix de localisation en 1999 et en 2007 a aussi permis de donner des éléments de réponse sur la transférabilité temporelle des modèles de choix de localisation et de questionner, dans les travaux futurs, le pouvoir prédictif d’un modèle de choix de localisation. / This thesis, focusing on the choice of residential location, is based on the theoretical framework of urban micro-economy and random utility. Though discrete choice modelling is the most appropriate in this field, the difficulty lies in choosing the appropriate model to the spatial context of residential location choice (spatial autocorrelation, large number of alternatives), on the one hand, and in the way of defining the spatial scale, on the other hand. For this purpose, we proceeded in two stages. We estimated a multinomial logit with random sampling of alternatives to understand the process of residential location choice before taking into account the spatial autocorrelation, and estimating a nested logit model. It also allowed to investigate the feasibility of applying a new method to correct biases of sampling alternatives in the case of nested logit model. In terms of results, we have shown that social environment are the most important determinants of residential location choice. Though job accessibility still weigh on household choice decision. In terms of methodology, we were able to test the feasibility of estimating a nested logit model with sampling of alternatives to analyze the choice of location of Lyon urban area. However, we could not overcome the difficulty of distinguishing spatial autocorrelation from nesting. The use of 1999 and 2007 databases to model residential location choice also helped to provide answers on the temporal transferability of location choice models and discuss in future work the predictive power of a location choice model.

Made available in DSpace on 2017-07-10T19:24:17Z (GMT). No. of bitstreams: 1 DENISE_M_GR_ZEGOZEWSKI.pdf: 8188144 bytes, checksum: 045f54782a1ea2161edf5aa7046a8c1c (MD5) Previous issue date: 2016-02-03 / Estimates of agricultural production are greatly important especially in economy field. However, they depend on area knowledge and cropping yield. Thus, this study aimed to propose a methodology to estimate the areas cropped with soybeans and corn in Paraná State according to multi-temporal EVI/MODIS vegetation index images for 2010/2011, 2011/2012 and 2012/2013 crop years. In addition, there was a research with spatial autocorrelation soybean yield in Paraná, with EVI vegetation index and meteorological variables in a decennial scale and estimate yield using CAR, SAR and GWR models. In Paraná State, there is a drawback to map soybeans crop since corn sowing period is very close to the first one. Therefore, images from the maximum and minimum vegetative vigour were drawn of each studied crop for mapping soybean and corn crops in order to obtain both cropping areas. Although, for the separation, Spectro Angle Mapper algorithm (SAM) was applied by one of the studied crops, while mapping was obtained by multiplying the other bands. Thus, for spatial statistics application of mapped data, the average EV profile of each municipality was extracted as well as for each multi-temporal image, in order to change them into a decennial scale. According to the spatial statistics of such areas, the descriptive analysis of univariate spatial autocorrelation (global and local) of each ten-day variable was used based on the soybean cycle. A bivariate autocorrelation analysis between soybean yield and the studied varieties were also performed. Finalizing the methodology, variables with the highest significant level by stepwise method were selected and SAR, CAR and GWR models were generated to estimate soybean yield. As results, regarding mappings, the following answers for soybean were found out: r = 0.95 and r = 0.99, and while for corn, the answers were: r = 0.72 and r = 0.95 for 2012/2013 and 2013/2014 crop years in relation to the official data from SEAB. So, it has been proved some great efficiency of this methodology to separate and identify crops. When the descriptive statistics of municipalities for each variable was carried out, it was found out that some regions began an early sowing in relation to other ones in Paraná by the decennial vegetation index. The ten-day scale was also possible to be identified according to the climatic factors that caused soybean yield damage. Based on the analysis of spatial autocorrelation, the greatest similarities occurred in 2011/2012 crop year, the one affected by the weather change, whose yields were similar in the municipalities of Paraná State. For spatial modelling, it was observed that selection of decennial variables was different for each studied crop year, and the best model selected by the validation. And GWR was chosen as the best model by the AIC, BIC and adjusted R² validation criteria. The residuals were randomly distributed throughout all the State, so that spatial autocorrelation could be eliminated. / As estimativas das produções agrícolas têm grande importância, principalmente, no âmbito econômico. No entanto, elas são dependentes do conhecimento da área de cultivo e da produtividade da cultura. Desta forma, este trabalho teve por objetivo propor uma metodologia para estimar as áreas cultivadas com soja e milho em escala municipal no Estado do Paraná a partir de imagens multi-temporais do índice de vegetação EVI/MODIS, para os anos-safras 2010/2011, 2011/2012 e 2012/2013. Além disto, trabalhar com a autocorrelação espacial da produtividade da soja nesse Estado, com o índice de vegetação EVI e variáveis agrometeorológicas em escala decendial bem como estimar a produtividade a partir dos modelos CAR, SAR e GWR. No Paraná, há o inconveniente para mapear a soja devido à proximidade de datas de semeadura do milho. Assim, para o mapeamento da soja e do milho, utilizaram-se imagens englobando o período de máximo e mínimo vigor vegetativo de cada cultura, para se obter a área cultivada das duas. Para a separação, utilizou-se o algoritmo Spectro Angle Mapper (SAM) para uma das culturas e obteve-se o mapeamento da outra pela multiplicação de bandas. Para aplicação da estatística espacial dos dados mapeados, extraiu-se o perfil médio do EVI de cada município e para cada imagem multi-temporal para transformá-los em escala decendial. De acordo com a estatística espacial de áreas, utilizou-se a análise descritiva, de autocorrelação espacial univariada (global e local) de cada variável decendial com foco no ciclo da soja. Também realizou-se a análise de autocorrelação bivariada entre a produtividade da soja com as variáveis em estudo. Finalizando a metodologia, selecionaram-se as variáveis com maior índice de significância pelo método de stepwise e, em seguida, foram gerados os modelos estimados (SAR, CAR e GWR) da produtividade da soja. Como resultados, foram encontradas as seguintes respostas para os mapeamentos da soja r= 0,95 e 0,99, e para o milho de r = 0,72 e r= 0,95 para os anos-safras 2012/2013 e 2013/2014 em relação aos dados oficiais da SEAB. Logo, comprovou-se a grande eficiência da metodologia para separação e identificação das culturas. Quando realizada a estatística descritiva dos municípios para cada variável, verificaram-se regiões que iniciam as semeaduras antecipadas em relação a outras regiões do Estado pelos decêndios do índice de vegetação. Foi também possível identificar os decêndios em que os fatores climáticos causaram danos à produtividade da soja. Na análise da autocorrelação espacial, as maiores similaridades ocorreram no ano-safra 2011/2012, ano afetado pela variação climática, cujas produtividades foram semelhantes nos municípios do Paraná. Para a modelagem espacial, verificou-se que a seleção das variáveis decêndiais foi diferente para cada ano-safra estudado, e o GWR foi escolhido como melhor modelo pelos critérios de validação, AIC, BIC e R² ajustado. Foram encontrados resíduos distribuídos aleatoriamente por todo o Estado, para que assim se eliminasse a autocorrelação espacial

A acessibilidade está relacionada com a maneira como a disponibilidade de transportes e os usos do solo afetam os indivíduos na realização de viagens para o desenvolvimento de suas atividades habituais. Freqüentemente se assume que os moradores de baixa renda da periferia são os mais afetados pela falta de acesso aos meios de transporte. A questão subjacente a esta afirmação, no entanto, permanece sem uma resposta definitiva: o nível de renda, por si só, seria um indicativo do nível de acessibilidade? O objetivo deste estudo é explorar a união de ferramentas de estatística espacial e SIG (Sistema de Informações Geográficas) com um propósito específico, que é o de analisar as relações entre aspectos da distribuição espacial de características da população (como a renda, por exemplo) de uma cidade média brasileira e os diversos níveis de acessibilidade por diferentes modos de transporte nela observados, buscando possíveis respostas para esta pergunta. Quando se utiliza procedimentos de visualização e classificação de dados espaciais comuns em SIG, nem sempre as informações são diretamente perceptíveis. Logo, deve-se utilizar ferramentas que ampliem as possibilidades de compreensão e análise dos dados. Inicialmente, as ferramentas selecionadas para uso neste trabalho são apresentadas e discutidas quanto à sua aplicação e utilização na análise proposta. Para tal foram utilizados dados coletados em uma pesquisa origem–destino (O-D) realizada na cidade de Bauru - SP, agrupados por setores censitários e adicionados ao SIG, aplicando técnicas de estatística espacial utilizadas para entidades do tipo área. Os resultados obtidos são apresentados na forma de mapas e de índices que medem a associação espacial global e local entre estas zonas. Uma das conclusões interessantes da aplicação foi a identificação de regiões da cidade com dinâmica particular, que contrariam o padrão global observado nas demais partes da área urbana. Pôde-se constatar ainda particularidades a respeito do uso de cada modo de transportes. O modo automóvel como motorista, por exemplo, possui agrupamento espacial bem definido no nível de renda alta tanto nas regiões de periferia, como nas de transição e central. Já o modo ônibus é predominantemente utilizado nas zonas de renda baixa das regiões de periferia e transição, enquanto que os modos não motorizados possuem uma dinâmica bem diversificada em toda a área urbana. Estes e outros resultados do estudo de caso deixam claro que as análises de estatística espacial em ambiente SIG criam uma ferramenta para ampliar a análise convencional de acessibilidade em transportes / Transportation accessibility is directly related to the level of transportation supply and land uses and the way they affect individuals in their trip desires for accomplishing regular-basis activities. It is often assumed that low-income segments of the population living at the periphery of the cities are those affected the most by poor conditions of transportation accessibility. There is a subjacent question behind this statement, however, which is: can the income level or the location of an individual alone explain his/her accessibility level? In order to look for answers to this question, the aim of this study is to analyze, making use of spatial statistics tools in a GIS (Geographic Information System) environment, the relationships between accessibility and income and their geographical distributions in a medium-sized Brazilian city. The application of the most commonly used GIS resources, such as visualization and spatial data classification tools, not always assures a full comprehension of the phenomenon under analysis. As a consequence, many problems require tools that enhance the possibilities of observation and analysis. As tools with this characteristic have been used in this work, they were initially introduced. Thereafter, the possibilities of use of these tools in the problem analyzed were also discussed. Data of an origin-destination (O-D) survey carried out in the city of Bauru, located in the state of São Paulo, which brings information about four different transportation modes, were used in this study. Such data, grouped following the census tracts, were carefully examined in a Geographic Information System in order to look for spatial patterns of accessibility that are not visible in the traditional approaches. The results of the analysis are presented in maps and as indices that are able to capture glabal and local spatial association patterns in areas. One of the interesting outcomes of the application was the identification of regions with particular dynamics, which go against the pattern found in the overall urban area. Particularities regarding each particular transportation mode have also been noticed. The zones where the automobile is most used (by drivers, not by passengers) are spatially clustered, regardless if the zone is at the periphery, transition zone or central area of the city. The bus trips are predominantly carried out in low-income areas of the periphery and transition rings, while the non-motorized modes (walk and bicycle) have shown a very diversified dynamics in the entire urban area. This and other results of the case study clearly indicate that spatial statistics analyses in a GIS environment create a powerful tool to extend conventional transportation accessibility analysis

Made available in DSpace on 2017-05-12T14:47:10Z (GMT). No. of bitstreams: 1 Ademir Natal Correa.pdf: 1505539 bytes, checksum: fd8e294f5766bf4043789d75eba28f1f (MD5) Previous issue date: 2007-07-16 / The objective of this study was to assess the relationship among soil physical attributes and their influences on wheat yield. For this purpose an estimating method, called State-Space Model or dynamic linear regression model, was used and compared to simple and multiple regression models of classical statistics. Experimental data were obtained at a Rhodic Ferralsol, originated from UNIOESTE Agricultural Engineering Experimental Nucleus Cascavel Campus, in an area where wheat was grown. In this area, 3 equally spaced transects, with 97 sampling points, 3.0 meters away from each other, were delimited. The State-Space approach was used to assess wheat yield estimate on position i, influenced by wheat yield, bulk density, soil compaction degree and soil resistance to penetration on position i-1 in different combination between data series of these variables. Applying the State-Space approach, all the response variables presented significant correlation with the dependent variable: soil resistance to penetration was the attribute with the best correlation, presenting R2 coefficient equal to 0.849. The other attributes had R2 coefficient of around 0.800. Comparing to conventional static models, soil resistance to penetration attribute had R2 coefficient equal to 0.102. The other attributes had R2 coefficient equal or less than 0.087, in conventional regression. Utilizing the State-Space approach, the two combinations that indicated the best results were: 1) between wheat yield and soil resistance to penetration that showed the best estimate to wheat yield with R2 coefficient equal to 0.849, while the same combination in conventional regression presented R2 equal to 0.102; 2) between wheat yield, soil compaction degree and soil resistance to penetration, with R2 coefficient equal to 0.836, while the same combination in classical regression presented R2 equal to 0.217. Thus, it is possible to show the advantage of the State-Space approach in relation to other more conventional regression methods for estimating and forecasting in soil-plant system relationship. / Este trabalho foi realizado com o objetivo de estudar o relacionamento entre os atributos físicos do solo e a influência destes na produtividade de trigo. Para isso, utilizou-se o método de estimação chamado de Modelo de Espaço de Estados ou modelo de regressão linear dinâmico, comparando-o aos modelos de regressão simples e múltipla da estatística clássica. Os dados experimentais foram obtidos em um Latossolo Vermelho-Escuro pertencente ao Núcleo Experimental de Engenharia Agrícola da Universidade Estadual do Oeste do Paraná Campus de Cascavel, em uma área cultivada com trigo. Foram demarcadas 3 transeções com 97 pontos de amostragem espaçados de 3 m entre si. A abordagem de Espaço de Estados foi usada para avaliar a estimativa da produtividade do trigo na posição i, influenciada por medidas da produtividade do trigo, da densidade do solo, do grau de compactação do solo e da resistência do solo à penetração na posição i-1, em diferentes combinações entre as séries de dados dessas variáveis. Com a aplicação da abordagem de Espaço de Estados, todas as variáveis explicativas utilizadas apresentaram correlação significativa com a variável dependente: a resistência do solo à penetração foi o atributo com a melhor correlação, apresentando o coeficiente de ajuste R2 igual a 0,849. Os demais atributos tiveram os coeficientes R2 em torno de 0,800. Comparando-se com os modelos estáticos convencionais, o atributo resistência do solo à penetração teve o coeficiente de ajuste R2 igual a 0,102 e os demais atributos tiveram os seus coeficientes R2 abaixo de 0,087, na regressão convencional. Utilizando a metodologia de Espaço de Estados, as duas combinações que indicaram os melhores resultados foram a combinação entre produtividade do trigo e resistência do solo à penetração, que apresentou a melhor estimativa para produtividade do trigo, com coeficiente R2 igual a 0,849. A mesma combinação na regressão convencional resultou em R2 igual a 0,102. A segunda melhor combinação ocorreu entre os atributos: produtividade do trigo, grau de compactação do solo e resistência do solo à penetração, com R2 igual a 0,836, sendo que a mesma combinação na regressão clássica teve o coeficiente R2 igual a 0,217. Com isso é possível mostrar-se a vantagem da abordagem de Espaço de Estados em relação a outros métodos de estimativa e previsão para o relacionamento no sistema solo-planta.

Made available in DSpace on 2017-05-12T14:47:34Z (GMT). No. of bitstreams: 1 DENISE_M_GR_ZEGOZEWSKI.pdf: 8188144 bytes, checksum: 045f54782a1ea2161edf5aa7046a8c1c (MD5) Previous issue date: 2016-02-03 / Estimates of agricultural production are greatly important especially in economy field. However, they depend on area knowledge and cropping yield. Thus, this study aimed to propose a methodology to estimate the areas cropped with soybeans and corn in Paraná State according to multi-temporal EVI/MODIS vegetation index images for 2010/2011, 2011/2012 and 2012/2013 crop years. In addition, there was a research with spatial autocorrelation soybean yield in Paraná, with EVI vegetation index and meteorological variables in a decennial scale and estimate yield using CAR, SAR and GWR models. In Paraná State, there is a drawback to map soybeans crop since corn sowing period is very close to the first one. Therefore, images from the maximum and minimum vegetative vigour were drawn of each studied crop for mapping soybean and corn crops in order to obtain both cropping areas. Although, for the separation, Spectro Angle Mapper algorithm (SAM) was applied by one of the studied crops, while mapping was obtained by multiplying the other bands. Thus, for spatial statistics application of mapped data, the average EV profile of each municipality was extracted as well as for each multi-temporal image, in order to change them into a decennial scale. According to the spatial statistics of such areas, the descriptive analysis of univariate spatial autocorrelation (global and local) of each ten-day variable was used based on the soybean cycle. A bivariate autocorrelation analysis between soybean yield and the studied varieties were also performed. Finalizing the methodology, variables with the highest significant level by stepwise method were selected and SAR, CAR and GWR models were generated to estimate soybean yield. As results, regarding mappings, the following answers for soybean were found out: r = 0.95 and r = 0.99, and while for corn, the answers were: r = 0.72 and r = 0.95 for 2012/2013 and 2013/2014 crop years in relation to the official data from SEAB. So, it has been proved some great efficiency of this methodology to separate and identify crops. When the descriptive statistics of municipalities for each variable was carried out, it was found out that some regions began an early sowing in relation to other ones in Paraná by the decennial vegetation index. The ten-day scale was also possible to be identified according to the climatic factors that caused soybean yield damage. Based on the analysis of spatial autocorrelation, the greatest similarities occurred in 2011/2012 crop year, the one affected by the weather change, whose yields were similar in the municipalities of Paraná State. For spatial modelling, it was observed that selection of decennial variables was different for each studied crop year, and the best model selected by the validation. And GWR was chosen as the best model by the AIC, BIC and adjusted R² validation criteria. The residuals were randomly distributed throughout all the State, so that spatial autocorrelation could be eliminated. / As estimativas das produções agrícolas têm grande importância, principalmente, no âmbito econômico. No entanto, elas são dependentes do conhecimento da área de cultivo e da produtividade da cultura. Desta forma, este trabalho teve por objetivo propor uma metodologia para estimar as áreas cultivadas com soja e milho em escala municipal no Estado do Paraná a partir de imagens multi-temporais do índice de vegetação EVI/MODIS, para os anos-safras 2010/2011, 2011/2012 e 2012/2013. Além disto, trabalhar com a autocorrelação espacial da produtividade da soja nesse Estado, com o índice de vegetação EVI e variáveis agrometeorológicas em escala decendial bem como estimar a produtividade a partir dos modelos CAR, SAR e GWR. No Paraná, há o inconveniente para mapear a soja devido à proximidade de datas de semeadura do milho. Assim, para o mapeamento da soja e do milho, utilizaram-se imagens englobando o período de máximo e mínimo vigor vegetativo de cada cultura, para se obter a área cultivada das duas. Para a separação, utilizou-se o algoritmo Spectro Angle Mapper (SAM) para uma das culturas e obteve-se o mapeamento da outra pela multiplicação de bandas. Para aplicação da estatística espacial dos dados mapeados, extraiu-se o perfil médio do EVI de cada município e para cada imagem multi-temporal para transformá-los em escala decendial. De acordo com a estatística espacial de áreas, utilizou-se a análise descritiva, de autocorrelação espacial univariada (global e local) de cada variável decendial com foco no ciclo da soja. Também realizou-se a análise de autocorrelação bivariada entre a produtividade da soja com as variáveis em estudo. Finalizando a metodologia, selecionaram-se as variáveis com maior índice de significância pelo método de stepwise e, em seguida, foram gerados os modelos estimados (SAR, CAR e GWR) da produtividade da soja. Como resultados, foram encontradas as seguintes respostas para os mapeamentos da soja r= 0,95 e 0,99, e para o milho de r = 0,72 e r= 0,95 para os anos-safras 2012/2013 e 2013/2014 em relação aos dados oficiais da SEAB. Logo, comprovou-se a grande eficiência da metodologia para separação e identificação das culturas. Quando realizada a estatística descritiva dos municípios para cada variável, verificaram-se regiões que iniciam as semeaduras antecipadas em relação a outras regiões do Estado pelos decêndios do índice de vegetação. Foi também possível identificar os decêndios em que os fatores climáticos causaram danos à produtividade da soja. Na análise da autocorrelação espacial, as maiores similaridades ocorreram no ano-safra 2011/2012, ano afetado pela variação climática, cujas produtividades foram semelhantes nos municípios do Paraná. Para a modelagem espacial, verificou-se que a seleção das variáveis decêndiais foi diferente para cada ano-safra estudado, e o GWR foi escolhido como melhor modelo pelos critérios de validação, AIC, BIC e R² ajustado. Foram encontrados resíduos distribuídos aleatoriamente por todo o Estado, para que assim se eliminasse a autocorrelação espacial

Abstract not available

In time series analysis, most of the models are based on the assumption of covariance stationarity. However, many time series in the applied sciences show a time-varying second-order structure. That is, variance and covariance, or equivalently the spectral structure, are likely to change over time. Examples may be found in a growing number of fields, such as biomedical time series analysis, geophysics, telecommunications, or financial data analysis, to name but a few. In this thesis, we are concerned with the modelling of such nonstationary time series, and with the subsequent questions of how to estimate their second-order structure and how to forecast these processes. We focus on univariate, discrete-time processes with zero-mean arising, for example, when the global trend has been removed from the data. The first chapter presents a simple model for nonstationarity, where only the variance is time-varying. This model follows the approach of "local stationarity" introduced by [1]. We show that our model satisfactorily explains the nonstationary behaviour of several economic data sets, among which are the U.S. stock returns and exchange rates. This chapter is based on [5]. In the second chapter, we study more complex models, where not only the variance is evolutionary. A typical example of these models is given by time-varying ARMA(p,q) processes, which are ARMA(p,q) with time-varying coefficients. Our aim is to fit such semiparametric models to some nonstationary data. Our data-driven estimator is constructed from a minimisation of a penalised contrast function, where the contrast function is an approximation to the Gaussian likelihood of the model. The theoretical performance of the estimator is analysed via non asymptotic risk bounds for the quadratic risk. In our results, we do not assume that the observed data follow the semiparamatric structure, that is our results hold in the misspecified case. The third chapter introduces a fully nonparametric model for local nonstationarity. This model is a wavelet-based model of local stationarity which enlarges the class of models defined by Nason et al. [3]. A notion of time-varying "wavelet spectrum' is uniquely defined as a wavelet-type transform of the autocovariance function with respect to so-called "autocorrelation wavelets'. This leads to a natural representation of the autocovariance which is localised on scales. One particularly interesting subcase arises when this representation is sparse, meaning that the nonstationary autocovariance may be decomposed in the autocorrelation wavelet basis using few coefficients. We present a new test of sparsity for the wavelet spectrum in Chapter 4. It is based on a non-asymptotic result on the deviations of a functional of a periodogram. In this chapter, we also present another application of this result given by the pointwise adaptive estimation of the wavelet spectrum. Chapters 3 and 4 are based on [6] Computational aspects of the test of sparsity and of the pointwise adaptive estimator are considered in Chapter 5. We give a description of a full algorithm, and an application in biostatistics. In this chapter, we also derive a new test of covariance stationarity, applied to another case study in biostatistics. This chapter is based on [7]. Finally, Chapter 6 address the problem how to forecast the general nonstationary process introduced in Chapter 3. We present a new predictor and derive the prediction equations as a generalisation of the Yule-Walker equations. We propose an automatic computational procedure for choosing the parameters of the forecasting algorithm. Then we apply the prediction algorithm to a meteorological data set. This chapter is based on [2,4]. References [1] Dahlhaus, R. (1997). Fitting time series models to nonstationary processes. Ann. Statist., 25, 1-37, 1997. [2] Fryzlewicz, P., Van Bellegem, S. and von Sachs, R. (2003). Forecasting non-stationary time series by wavelet process modelling. Annals of the Institute of Statistical Mathematics. 55, 737-764. [3] Nason, G.P., von Sachs, R. and Kroisandt, G. (2000). Wavelet processes and adaptive estimation of evolutionary wavelet spectra. Journal of the Royal Statistical Society Series B. 62, 271-292. [4] Van Bellegem, S., Fryzlewicz, P. and von Sachs, R. (2003). A wavelet-based model for forecasting non-stationary processes. In J-P. Gazeau, R. Kerner, J-P. Antoine, S. Metens and J-Y. Thibon (Eds.). GROUP 24: Physical and Mathematical Aspects of Symmetries. Bristol: IOP Publishing (in press). [5] Van Bellegem, S. and von Sachs, R. (2003). Forecasting economic time series with unconditional time-varying variance. International Journal of Forecasting (in press). [6] Van Bellegem, S. and von Sachs, R. (2003). Locally adaptive estimation of sparse, evolutionary wavelet spectra (submitted). [7] Van Bellegem, S. and von Sachs, R. (2003). On adaptive estimation for locally stationary wavelet processes and its applications (submitted).

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Print quality demands for coated papers are steadily growing, and achieving coating uniformity is crucial for high image sharpness, colour fidelity, and print uniformity. Coating uniformity may be divided into two scales: coating thickness uniformity and coating microstructure uniformity, the latter of which includes pigment, pore and binder distributions within the coating layer. This thesis concerns the investigation of both types of coating uniformity by using an approach of quantitative microscopy.First, coating thickness uniformity was analysed by using scanning electron microscope (SEM) images of paper cross sections, and the relationships between local coating thickness variations and the variations of underlying base sheet structures were determined. Special attention was given to the effect of length scales on the coating thickness vs. base sheet structure relationships.The experimental results showed that coating thickness had a strong correlation with surface height (profile) of base sheet at a small length scale. However, at a large length scale, it was mass density of base sheet (formation) that had the strongest correlation with coating thickness. This result explains well the discrepancies found in the literature for the relationship between coating thickness variation and base sheet structure variations. The total variance of coating thickness, however, was dominated by the surface height variation in the small scale, which explained around 50% of the variation. Autocorrelation analyses were further performed for the same data set. The autocorrelation functions showed a close resemblance of the one for a random shot process with a correlation length in the order of fibre width. All these results suggest that coating thickness variations are the result of random deposition of particles with the correlation length determined by the base sheet surface textures, such as fibre width.In order to obtain fundamental understandings of the random deposition processes on a rough surface, such as in paper, a generic particle deposition model was developed, and systematic analyses were performed for the effects of particle size, coat weight (average number of particles), levelling, and system size on coating thickness variation. The results showed that coating thickness variation3grows with coat weight, but beyond a certain coat weight, it reaches a plateau value. A scaling analysis yielded a universal relationship between coating thickness variation and the above mentioned variables. The correlation length of coating thickness was found to be determined by average coat weight and the state of underlying surfaces. For a rough surface at relatively low coat weight, the correlation length was typically in the range of fibre width, as was also observed experimentally.Non-uniformities within the coating layer, such as porosity variations and binder distributions, are investigated by using a newly developed method: field emission scanning electron microscopy (FESEM) in combination with argon ion beam milling technique. The combination of these two techniques produced extremely high quality images with very few artefacts, which are particularly suited for quantitative analyses of coating structures. A new evaluation method was also developed by using marker-controlled watershed segmentation (MCWS) of the secondary electron images (SEI).The high resolution imaging revealed that binder enrichment, a long disputed subject in the area, is present in a thin layer of a 500 nm thickness both at the coating surface and at the base sheet/coating interface. It was also found that the binders almost exclusively fill up the small pores, whereas the larger pores are mainly empty or depleted of binder.