Wavelet-based estimators for mixture regression

Author(s)

Montoril, Michel H. ^[1] ; Pinheiro, Aluisio ^[2] ; Vidakovic, Brani ^[3]

Affiliation

^[1] Univ Fed Juiz de Fora, Dept Stat, BR-36036330 Juiz De Fora - Brazil

^[2] Univ Estadual Campinas, Dept Stat, Campinas, SP - Brazil

^[3] Georgia Inst Technol, H Milton Stewart Sch Ind & Syst Engn, Atlanta, GA 30332 - USA

• Document type: Journal article
• Source: SCANDINAVIAN JOURNAL OF STATISTICS; v. 46, n. 1, p. 215-234, MAR 2019.
• Web of Science Citations: 0

Abstract

We consider a process that is observed as a mixture of two random distributions, where the mixing probability is an unknown function of time. The setup is built upon a wavelet-based mixture regression. Two linear wavelet estimators are proposed. Furthermore, we consider three regularizing procedures for each of the two wavelet methods. We also discuss regularity conditions under which the consistency of the wavelet methods is attained and derive rates of convergence for the proposed estimators. A Monte Carlo simulation study is conducted to illustrate the performance of the estimators. Various scenarios for the mixing probability function are used in the simulations, in addition to a range of sample sizes and resolution levels. We apply the proposed methods to a data set consisting of array Comparative Genomic Hybridization from glioblastoma cancer studies. (AU)

• FAPESP's process: 13/09035-1 - Regression models in functional data analysis
• Grantee: Michel Helcias Montoril
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/21273-5 - Estimation of semi-functional linear models by wavelets
• Grantee: Michel Helcias Montoril
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 13/00506-1 - Time series, wavelets and functional data analysis
• Grantee: Pedro Alberto Morettin
• Support Opportunities: Research Projects - Thematic Grants