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Doctoral Thesis
DOI
10.11606/T.45.2013.tde-04042013-215702
Document
Author
Full name
Michel Helcias Montoril
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Morettin, Pedro Alberto (President)
Chiann, Chang
Dias, Ronaldo
Pinheiro, Aluísio de Souza
Sato, João Ricardo
Title in Portuguese
Modelos de regressão com coeficientes funcionais para séries temporais
Keywords in Portuguese
algoritmo de Daubechies--Lagarias
modelos de regressão com coeficientes funcionais.
ondaletas clássicas
ondaletas deformadas
Splines
Abstract in Portuguese
Nesta tese, consideramos o ajuste de modelos de regressão com coeficientes funcionais para séries temporais, por meio de splines, ondaletas clássicas e ondaletas deformadas. Consideramos os casos em que os erros do modelo são independentes e correlacionados. Através das três abordagens de estimação, obtemos taxas de convergência a zero para distâncias médias entre as funções do modelo e seus respectivos estimadores, propostos neste trabalho. No caso das abordagens de ondaletas (clássicas e deformadas), obtemos também resultados assintóticos em situações mais específicas, nas quais as funções do modelo pertencem a espaços de Sobolev e espaços de Besov. Além disso, estudos de simulação de Monte Carlo e aplicações a dados reais são apresentados. Por meio desses estudos numéricos, fazemos comparações entre as três abordagens de estimação propostas, e comparações entre outras abordagens já conhecidas na literatura, onde verificamos desempenhos satisfatórios, no sentido das abordagens propostas fornecerem resultados competitivos, quando comparados aos resultados oriundos de metodologias já utilizadas na literatura.
Title in English
Functional-coefficient regression models for time series
Keywords in English
Daubechies--Lagarias algorithm
functional-coefficient regression models.
Splines
warped wavelets
wavelets
Abstract in English
In this thesis, we study about fitting functional-coefficient regression models for time series, by splines, wavelets and warped wavelets. We consider models with independent and correlated errors. Through the three estimation approaches, we obtain rates of convergence to zero for average distances between the functions of the model and their estimators proposed in this work. In the case of (warped) wavelets approach, we also obtain asymptotic results in more specific situations, in which the functions of the model belong to Sobolev and Besov spaces. Moreover, Monte Carlo simulation studies and applications to real data sets are presented. Through these numerical results, we make comparisons between the three estimation approaches proposed here and comparisons between other approaches known in the literature, where we verify interesting performances in the sense that the proposed approaches provide competitive results compared to the results from methodologies used in literature.
 
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Tese_Montoril.pdf (4.43 Mbytes)
Publishing Date
2013-04-15
 
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