The autocorrelation function is a basic tool for time series analysis. The clas- sical estimation is very sensitive to outliers and can lead to misleading results. This thesis deals with robust estimations of the autocorrelation function, which is more resistant to the outliers than the classical estimation. There are presen- ted following approaches: leaving out the outliers from the data, replacement the average with the median, data transformation, the estimation of another coeffici- ent, robust estimation of the partial autocorrelation function or linear regression. The thesis describes the applicability of the presented methods, their advantages and disadvantages and necessary assumptions. All the approaches are compared in simulation study and applied to real financial data. 1

Volcanic rifting environments, such as in Iceland, are challenging for conventional seismic reflection methods using active surface seismic sources. This study demonstrates the potential of a novel technique, called Virtual Reflection Seismic Profiling (VRSP) for imaging reflections in geothermal regions, like Hverahlíð, where a dense seismic array recorded a number of local microearthquakes for cross-correlation. Uppsala University, in collaboration with Reykjavik Energy, recorded seismicity in Hverahlíð using both seismometers and geophones. Acquired data were processed using the VRSP method, which applies seismic interferometry only to selected events, in this thesis local microearthquakes. Cross-correlation of the signal from a microearthquake recorded at one of the stations, which acts as a virtual source, with a ghost reflection recorded by the remaining receivers, produces a virtual shot gather. Stacking each station’s result, for all available events, and following a conventional multichannel processing sequence resulted in two stacked seismic images. Potential reflections observed in the obtained sections could be associated with major feed zones identified in the area by the borehole measurements. Eight dynamite explosions were processed with a conventional seismic reflection method, as a complementary source to the microearthquakes. In the produced stacked seismic section two potential reflections could be observed. Results from both passive and active datasets were 3D visualised to verify whether the reflections correspond to each other between sections. Two horizons were traced throughout all three stacked sections. One more interface appeared on two images obtained from processing the passive data. This study shows promising results for using natural sources to image the subsurface in a challenging environment.

The efficient market hypothesis states that stock prices fully reflect availablei nformation and that stocks thereby always are priced correctly. Hence, it should be impossible to predict future prices in the stock market, and investors will gain no benefits from engaging themselves into historical analyzes. This is a quantitative study which aim to investigate if there is any difference in market efficiency in Nordic stock markets during and after the financial crisis of 2008. By applying various statistical methods, such as unitroot tests, autocorrelation tests and runs test on the returns from each country’s leading market index, the study tries to find evidence for or against the weak form of market efficiency. The study finds evidence both for and against weak form market efficiency but concludes that there is no distinct difference in market efficiency during and after the financial crisis.

Ce mémoire de thèse concerne l’identification des facteurs de risque d’une maladie spécifique présentant une hétérogénéité spatiale au sein d’une région donnée. Plus particulièrement,nous nous sommes intéressés aux cancers des voies aéro-digestives supérieures(VADS) dans la région Nord-Pas-de-Calais (NPDC) en France. Pour cela, une étude cas témoins a d’abord été réalisée à partir de la création d’un échantillon d’individus sains qui n’étaient pas affectés par des tumeurs cancéreuses (les témoins) et d’un échantillon d’individus atteints du cancer (les cas - ou patients), recrutés dans les centres de soins dans le cadre des projets de recherche DEREDIA et NOFARIS. Concernant la méthodologie,des modèles binaires spatiaux répondant à l’objectif ont été développés à partir de travaux issus des domaines de recherche en statistique/économétrie des comportements(analyse des décisions) ainsi qu’en statistique spatiale. Un des apports méthodologiques de la thèse repose sur la combinaison de techniques provenant de ces deux champs de recherche. Dans une première partie, nous avons utilisé un modèle spatial binaire paramétrique contenant une variable spatiale latente de choix dans le cadre d’un échantillonnage des données. Ce problème est connu sous le nom de "Choice-Based Sampling" (CBS) dans les modèles discrets. Contrairement à l’échantillon aléatoire où tous les éléments de la population ont la même probabilité d’être choisi, l’échantillonnage CBS dans le modèle discret est un type d’échantillonnage dans lequel la classification de la population est faite sous forme de sous-ensembles (strates) basés sur des choix alternatifs. Dans ce contexte,l’utilisation de la procédure d’estimation par maximum de vraisemblance standard (MLE)dans le CBS pourrait mener à des estimations incohérentes (asymptotiquement biaisées).Nous avons adopté ainsi le principe du maximum de vraisemblance auprès de l’étude de scas-témoins spatiaux. Nous avons également fourni un estimateur des moments généralisés(GMM), basé sur les résidus généralisés. Dans une seconde partie, un modèle spatial binaire semi-paramétrique a été considéré. Nous présentons dans ces parties, une simulation de Monte Carlo pour étudier la performance des méthodes d’estimation au sein d’un échantillon final, que nous avons ensuite appliqué aux données du cancer VADS dans la région Nord-Pas-de-Calais. La troisième partie est consacrée à l’étude d’une fonction de risque spatiale en présence de données entachées d’erreurs. En effet, dans le cadre des données cas-témoins considérées, nous supposons que certaines données de type déclarative ne soient pas correctes. Une application de cette méthode à la cartographie du risque de développer un cancer VADS dans la région Nord-Pas-de-Calais a été étudiée. La dernière partie est consacrée à un modèle de durée spatial et son application aux données considérées. / This thesis concerns the identification of risk factors for a certain type of diseasepresenting a certain spatial heterogeneity in a given region.. More specifically, we are interested in cancers of the upper aerodigestive tract (UADT) cancers in the Nord-Pasde-Calais region (NPDC), France. For this, a case-control study was first carried out bycreating a sample of healthy individuals who are not affected by cancerous tumors (thecontrols) and a sample of individuals with cancer (Cases or patients), recruited in healthcenters as part of DEREDIA and NOFARIS research projects. From a methodologicalpoint of view, spatial binary models which meet the objective have been developed onthe basis of studies in statistical/behavioral econometrics (decision analysis) and spatialstatistics. One of the methodological contributions of the thesis on this plan is the combinationof techniques from these two fields of research.In the first part, we used a spatial binary parametric models containing spatial latentchoice variable in a context of sampling data. This problem is known as Choice-BasedSampling (CBS) in discrete choice model. Unlike the random sample where all items in the population have the same probability of being chosen, the Choice-Based Sampling indiscrete choice model is a type of sampling where the classification of the population intosubsets to be sampled is based on the choices or outcomes. In this context, the use ofstandard Maximum likelihood estimation (MLE) procedure in CBS could lead to an inconsistent(asymptotically biased) estimation. Thus, we adapt the principle of maximumlikelihood in our context of spatial case-control studies. We also provide a GMM estimatorbased on the generalized residuals.In the second part, a spatial semi-parametric binary model was considered. We present inthese parts a Monte Carlo experiment to investigate the finite sample performance of theseestimation methods, then we apply to the (UADT) cancer data in the Nord-Pas-de-Calaisregion.The third part is devoted to the study of a spatial risk function in the presence of datacontaminated by measurement errors. Indeed, in the context of the considered case-controlstudy, it is very likely that certain data transmitted by the patients is not correct. Anapplication of this method to the mapping of the risk of having UADT cancer in the Nord-Pas-de-Calais region was studied. The last part is devoted to a spatial duration modeland its application to the real data was considered.

In this study, we extend the spatial weight matrix defined by Getis and Aldstadt (2004) to a more general case. The modified spatial weight matrix performs better than the original spatial weight matrix since the modified spatial weight matrix adjusts weights of observations based on the distance from other observations. Both the simulation study and the application to the ecological process of invasion of non-native invasive plants (NNIPs) provide evidences for the better performance of the modified spatial weight matrix. We also develop procedures that can be used to quantify the invasion stages of NNIPs. The resultant map of invasion stage on county-level provides a useful and meaningful tool for policy makers; especially, it can be used to optimize allocation of management resources. The result of simultaneous autoregressive model shows that not only the biotic and abiotic factors but also human activities play an important role in the establishment and spread of multiflora rose in the Upper Midwest. It also shows the tendency of the establishment and spread of multiflora rose (Rosa Multiflora, Thunb. ex Murr.) in the Upper Midwest.

The empirical paper studies the relationship between property value and hedonic attributes. To indentify the determinant characteristics the influent the private real estate price, their degrees of significance and help with the valuation procedure, 8870 private residential property transactions with caveats lodged across country are selected from Urban Redevelopment Authority of Singapore. 40 models are tested and RMSE, R-Square, Adjusted R-Square, F-Value tests are performed to discover the overall fitness of the models. Breusch-Pagan F-Test is performed to test the existence of heteroskedasticity and VIF test to check multicolinearity. Z score is performed to check the spatial autocorrelation. Three founding are discovered. Firstly, size, age, floor level, population density level, latitude and construction status are core attributes resulting from the regression. Secondly, new district zones classified by functions are detected instead of 28 administrative districts. Thirdly, government policies and local customs (Feng Shui) are proven to be determinant variables as well. Two suggestions are given to regulate the market in the end of this article.

This dissertation investigates the effects of autocorrelation on the performances of various sampling plans for control charts in detecting special causes that may produce sustained or transient shifts in the process mean and/or variance. Observations from the process are modeled as a first-order autoregressive process plus a random error. Combinations of two Shewhart control charts and combinations of two exponentially weighted moving average (EWMA) control charts based on both the original observations and on the process residuals are considered. Three types of sampling plans are investigated: samples of n = 1, samples of n > 1 observations taken together at one sampling point, or samples of n > 1 observations taken at different times. In comparing these sampling plans it is assumed that the sampling rate in terms of the number of observations per unit time is fixed, so taking samples of n = 1 allows more frequent plotting. The best overall performance of sampling plans for control charts in detecting both sustained and transient shifts in the process is obtained by taking samples of n = 1 and using an EWMA chart combination with a observations chart for mean and a residuals chart for variance. The Shewhart chart combination with the best overall performance, though inferior to the EWMA chart combination, is based on samples of n > 1 taken at different times and with a observations chart for mean and a residuals chart for variance. / Ph. D.

We study the unusual phases seen in charge transfer salts (CTS) at 1/2 and 1/4 filling. We use the Holstein-Hubbard model (HHM) and the Peierls extended Hubbard model (PEH) to study competing phases in CTS. In the 1/2illed HHM the Holstein coupling promotes a Peierls charge-density wave phase while the on-site Coulomb repulsion U gives rise to antiferromagnetic correlations and a Mott insulating state. Takada et al. have shown possibility of a third metallic phase between the Mott and the Peierls phase. We investigate the presence of an intermediate phase between the Mott and Peierls phase using Stochastic Series Expansion (SSE) method. We used charge and spin susceptibilities to determine the phase boundaries. As the coupling is increased a spin gap opens followed by the Peierls transition. The intermediate phase is metallic and has a spin gap but no charge gap. Transitions from the Mott to intermediate and intermediate to Peierls state are Kosterlitz-Thouless type (KT). As the coulomb repulsion is increaed beyond certain value the two KT transitions fuse to give a single first order transition. Similar behavior is seen at 1/4illed HHM. We also studied the temperature dependence of charge ordering (CO) in 1/4illed CTS. Most previous theoretical studies of the on CTS have concentrated on ground state or T=0 properties. Here we show the evolution of charge ordered (CO) state with temperature and directly related the experimental phase diagram with our theoretical results. Our calculations show that as temperature is lowered the Wigner crystal state gives way to spin-Peierls state with a different pattern of CO. Also we show that the critical value of nearest neighbor Coulomb repulsion is depends on the total spin and is different for different spin subspace.

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This research work is focused on the balanced and partially balanced incomplete block designs when observations within blocks are correlated. The topic for this dissertation was motivated by a problem in pharmaceutical research, when several treatments are allocated to individuals, and repeated measurements are taken on each individual. In that case, there is correlation among the observations taken on the same individual. Typically, it is reasonable to assume that the observations within individual close to each other are highly correlated than observations that are far away from each other. It is also reasonable to assume that the correlation between any two observations within each individual is same. We have characterized balanced and partially balanced incomplete block designs when observations within blocks are autocorrelated. In Chapter 3, we have provided an explicit expression for the average variance of estimated elementary treatment contrasts for designs obtained by Type I and II series of orthogonal arrays, under autocorrelated errors, and compared them with the corresponding balanced incomplete block designs with uncorrelated errors. The relative efficiency of balanced incomplete block design compared to the corresponding balanced incomplete block design obtained by Types I and II series of orthogonal array under autocorrelated errors does not depend on the number of treatments (v) and is an increasing function of the block size (k). When orthogonal arrays of Type I or Type II do not exist for a given number of treatments, we provided alternative partially balanced designs with autocorrelated errors. In Chapter 4, we rearranged the treatments in each block of symmetric balanced incomplete block designs and used them with autocorrelated error structure of the plots in a block. The C-matrix of estimated treatment effects under autocorrelation was given and the relative efficiency of symmetric balanced incomplete block designs with independent errors compared to the autocorrelated designs is given. In Chapter 5, we discussed the compound symmetry correlation structure within blocks. An explicit expression of the average variance of designs obtained by Type I and II series of orthogonal arrays and symmetric balanced incomplete block designs under compound symmetric errors has been provided and compared them with the corresponding balanced incomplete block designs with uncorrelated errors. Finally, the relative efficiencies of these designs with autocorrelated errors vs. compound symmetric error structure are given / Statistics