Detection of similar successive groups in a model with diverging number of variable groups. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Ciuperca, Gabriela; Maciak, Matúš; Wahl, François
• Is Part Of: Sequential analysis. Volume 39:Issue 1(2020)
• Page Start: 92
• Page End: 114
• Publication Date: 2020-01-02
• Subjects: Adaptive penalty -- different successive groups -- diverging-dimensional group model -- fused group; 62F12 -- 62F35 -- 62J07; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2020.1726687
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: In this article, a linear model with grouped explanatory variables is considered. The idea is to perform an automatic detection of different successive groups of the unknown coefficients under the assumption that the number of groups is of the same order as the sample size. The standard least squares loss function and the quantile loss function are both used together with the fused and adaptive fused penalty to simultaneously estimate and group the unknown parameters. The proper convergence rate is given for the obtained estimators and the upper bound for the number of different successive group is derived. A simulation study is used to compare the empirical performance of the proposed fused and adaptive fused estimators, and a real application on the air quality data demonstrates the practical applicability of the proposed methods.