Detection of similar successive groups in a model with diverging number of variable groups

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.