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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Nonparametric regression with warped wavelets and strong mixing processes

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Autor(es):
Gomez, Luz M. [1] ; Porto, Rogerio F. [2] ; Morettin, Pedro A. [1]
Número total de Autores: 3
Afiliação do(s) autor(es):
[1] Univ Sao Paulo, Inst Math & Stat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
[2] Bank Brazil, SAUN Quadra 5, Lote B, Green Towers, BR-70742010 Brasilia, DF - Brazil
Número total de Afiliações: 2
Tipo de documento: Artigo Científico
Fonte: ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS; MAR 2021.
Citações Web of Science: 1
Resumo

We consider the situation of a univariate nonparametric regression where either the Gaussian error or the predictor follows a stationary strong mixing stochastic process and the other term follows an independent and identically distributed sequence. Also, we estimate the regression function by expanding it in a wavelet basis and applying a hard threshold to the coefficients. Since the observations of the predictor are unequally distant from each other, we work with wavelets warped by the density of the predictor variable. This choice enables us to retain some theoretical and computational properties of wavelets. We propose a unique estimator and show that some of its properties are the same for both model specifications. Specifically, in both cases the coefficients are unbiased and their variances decay at the same rate. Also the risk of the estimator, measured by the mean integrated square error is almost minimax and its maxiset remains unaltered. Simulations and an application illustrate the similarities and differences of the proposed estimator in both situations. (AU)

Processo FAPESP: 19/23078-1 - Análise da população de idosos em serviços de emergência
Beneficiário:Luz Marina Gómez Gómez
Linha de fomento: Bolsas no Brasil - Pós-Doutorado
Processo FAPESP: 18/04654-9 - Séries temporais, ondaletas e dados de alta dimensão
Beneficiário:Pedro Alberto Morettin
Linha de fomento: Auxílio à Pesquisa - Temático