This thesis presents a contribution to the active research area of functional data analysis (FDA) and is concerned with the analysis of data from complex experimental designs in which the responses are curves. High resolution, closely correlated data sets are encountered in many research fields, but current statistical methodologies often analyse simplistic summary measures and therefore limit the completeness and accuracy of conclusions drawn. Specifically the nature of the curves and experimental design are not taken into account. Mathematically, such curves can be modelled either as sample paths of a stochastic process or as random elements in a Hilbert space. Despite this more complex type of response, the structure of experiments which yield functional data is often the same as in classical experimentation. Thus, classical experimental design principles and results can be adapted to the FDA setting. More specifically, we are interested in the functional analysis of variance (ANOVA) of experiments which use orthogonal designs. Most of the existing functional ANOVA approaches consider only completely randomised designs. However, we are interested in more complex experimental arrangements such as, for example, split-plot and row-column designs. Similar to univariate responses, such complex designs imply that the response curves for different observational units are correlated. We use the design to derive a functional mixed-effects model and adapt the classical projection approach in order to derive the functional ANOVA. As a main result, we derive new functional F tests for hypotheses about treatment effects in the appropriate strata of the design. The approximate null distribution of these tests is derived by applying the Karhunen- Lo`eve expansion to the covariance functions in the relevant strata. These results extend existing work on functional F tests for completely randomised designs. The methodology developed in the thesis has wide applicability. In particular, we consider novel applications of functional F tests to gait analysis. Results are presented for two empirical studies. In the first study, gait data of patients with cerebral palsy were collected during barefoot walking and walking with ankle-foot orthoses. The effects of ankle-foot orthoses are assessed by functional F tests and compared with pointwise F tests and the traditional univariate repeated-measurements ANOVA. The second study is a designed experiment in which a split-plot design was used to collect gait data from healthy subjects. This is commonly done in gait research in order to better understand, for example, the effects of orthoses while avoiding confounded analysis from the high variability observed in abnormal gait. Moreover, from a technical point of view the study may be regarded as a real-world alternative to simulation studies. By using healthy individuals it is possible to collect data which are in better agreement with the underlying model assumptions. The penultimate chapter of the thesis presents a qualitative study with clinical experts to investigate the utility of gait analysis for the management of cerebral palsy. We explore potential pathways by which the statistical analyses in the thesis might influence patient outcomes. The thesis has six chapters. After describing motivation and introduction in Chapter 1, mathematical representations of functional data are presented in Chapter 2. Chapter 3 considers orthogonal designs in the context of functional data analysis. New functional F tests for complex designs are derived in Chapter 4 and applied in two gait studies. Chapter 5 is devoted to a qualitative study. The thesis concludes with a discussion which details the extent to which the research question has been addressed, the limitations of the work and the degree to which it has been answered.

Orientador: Fernando Roberto Martins / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Biologia / Made available in DSpace on 2018-08-23T02:32:50Z (GMT). No. of bitstreams: 1 VanMelis_Juliano_D.pdf: 2552550 bytes, checksum: 8227a941fa221a10cce8b272ae92449f (MD5) Previous issue date: 2013 / Resumo: Apesar da importância que as trepadeiras apresentam em florestas tropicais, estudos sobre a montagem da comunidade de lianas (trepadeiras lenhosas e sublenhosas) que investiguem desde a contribuição dos fatores abióticos e bióticos até fatores intrínsecos (coexistência entre indivíduos) são escassos. O objetivo geral desta tese é pesquisar a estruturação da comunidade das espécies de lianas em uma Floresta Estacional Semidecídua (FES), investigando (1) a importância relativa dos fatores ambientais e espaciais para diferentes espécies de lianas, (2) a estruturação filogenética da comunidade de trepadeiras em diferentes ambientes, e (3) os efeitos diretos ou mediados das árvores e arbustos para o número de espécies e indivíduos de trepadeiras. Mostramos que (1) grande parte da variação na composição de espécies de lianas em uma FES é devido a fatores não investigados (fatores estocásticos) e o espaço (autocorrelação espacial). Portanto, concluímos que os maiores determinantes na variação da composição de espécies de lianas em uma FES é a aleatoriedade (sendo reflexo da variação estocástica das populações) e a limitação por dispersão (demonstrada pela alta autocorrelação espacial). No segundo capítulo (2), encontramos que uma maioria discreta das parcelas apresentou maior aproximação filogenética do que o esperado ao acaso na comunidade de trepadeiras amostrada. Houve pouca influência de variáveis relacionadas à dinâmica florestal na variação da aproximação filogenética, sendo que áreas com árvores mais altas e maior proporção de árvores do presente apresentavam maior aproximação filogenética que outras áreas. Concluímos que em áreas de dossel mais baixo e menor proporção de árvores do presente (clareiras) não apresentam menor sinal filogenético, pois todas as espécies de lianas apresentariam potencial de existirem nestas áreas, enquanto que nas áreas de floresta madura haveria a existência de filtros ambientais para a existência de poucos ramos filogenéticos. Por último (3), encontramos que os atributos da comunidade de árvores e arbustos são fatores importantes na variação dos atributos da comunidade de lianas, sendo parte dele decorrente do distúrbio no dossel. Mas o distúrbio no dossel como fator direto é mais importante na variação da abundância e número de espécies de lianas em uma Floresta Estacional Semidecídua / Abstract: Despite the fact that climbing plants present in tropical forests, studies which investigate the contribution of abiotic and biotic factors or intrinsic factors (coexistence between individuals) on community assembly of lianas (woody and sub-woody climbers) are scarce. The overall objective of this thesis is to research the community structure of liana species in a Seasonal Semideciduous Forest (SSF), investigating (1) the relative importance of environmental and spatial factors on community assembly of lianas, (2) the phylogenetic structure of climbing plants community along the forest development (treefall gaps to old-growth forest), and (3) the direct or indirect effects of trees and shrubs for the number of species and individuals of climbing plants. We show that (1) much of the variation in species composition of lianas in a SSF is due to stochastic factors and space. Therefore, we conclude that the major determinants of variation in lianas' species composition in a TSF are stochastic variance of populations, shown by the unexplained factors, and dispersion limitation, shown by spatial autocorrelation. In the second chapter (2), we found that a slight majority of the sample plots showed cluster phylogenetic structure in the climbing plants community. There was a slight influence of variables related to forest dynamics in the variation of the phylogenetic structure, and areas with tall trees and higher proportion of present trees had higher values of clustering in phylogenetic structure than other areas. We conclude that in areas of lower canopy and smaller proportion of present trees (treefall gaps) showed few phylogenetic branches, since all species of climbing plants would be existing in these areas, while areas of old-growth forest would demonstrate environmental filters for the climbing plants. Finally, we also found (3) that the community of trees and shrubs' attributes (abundance and species richness) are important factors in the variation of attributes liana community (species richness and abundance), being part of it due to the canopy disturbance. But canopy disturbance was the more important direct factor in variance of abundance and species richness of lianas in a Seasonal Semideciduous Forest / Doutorado / Doutor em Biologia Vegetal

Orientador: Aluísio de Souza Pinheiro / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T09:39:03Z (GMT). No. of bitstreams: 1 Kist_Airton_D.pdf: 4639620 bytes, checksum: 2a0cc586e73dd5d71aa0eacf07be101d (MD5) Previous issue date: 2011 / Resumo: O problema de estimação funcional vem sendo estudado de formas variadas na literatura. Uma possibilidade bastante promissora se dá pela utilização de bases ortonormais de wavelets (ondaletas). Essa solução _e interessante por sua: frugalidade; otimalidade assintótica; e velocidade computacional. O objetivo principal do trabalho é estender os testes do modelo FANOVA de efeitos fixos, com erros i.i.d., baseados em ondaletas propostos em Abramovich et al. (2004), para modelos FANOVA de efeitos fixos com erros dependentes. Propomos um procedimento iterativo tipo Cocharane-Orcutt para estimar os parâmetros e a função. A função é estimada de forma não paramétrica via estimador ondaleta que limiariza termo a termo ou estimador linear núcleo ondaleta. Mostramos que, com erros i.i.d., a convergência individual do estimador núcleo ondaleta em pontos diádicos para uma variável aleatória com distribuição normal implica na convergência conjunta deste vetor para uma variável aleatória com distribuição normal multivariada. Além disso, mostramos a convergência em erro quadrático do estimador nos pontos diádicos. Sob uma restrição é possível mostrar que este estimador converge nos pontos diádicos para uma variável com distribuição normal mesmo quando os erros são correlacionados. O vetor das convergências individuais também converge para uma variável normal multivariada / Abstract: The functional estimation problem has been studied variously in the literature. A promising possibility is by use of orthonormal bases of wavelets. This solution is appealing because of its: frugality, asymptotic optimality, and computational speed. The main objective of the work is to extend the tests of fixed effects FANOVA model with iid errors, based on wavelet proposed in Abramovich et al. (2004) to fixed effects FANOVA models with dependent errors. We propose an iterative procedure Cocharane-Orcutt type to estimate the parameters and function. The function is estimated through a nonparametric wavelet estimator that thresholded term by term or wavelet kernel linear estimator. We show that, with iid errors, the individual convergence of the wavelet kernel estimator in dyadic points for a random variable with normal distribution implies the joint convergence of this vector to a random variable with multivariate normal distribution. Furthermore, we show the convergence of the squared error estimator in the dyadic points. Under a restriction is possible to show that this estimator converges in dyadic points to a variable with normal distribution even when errors are correlated. The vector of individual convergences also converges to a multivariate normal variable / Doutorado / Estatistica / Doutor em Estatística