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

## TL;DR

This paper introduces a method for automatically detecting successive groups of coefficients in a linear model with diverging group numbers, using fused penalties and providing theoretical guarantees and practical validation.

## Contribution

It proposes a novel approach combining fused and adaptive fused penalties for simultaneous estimation and grouping of coefficients in high-dimensional linear models.

## Key findings

- The estimators achieve a specified convergence rate.
- An upper bound for the number of groups is derived.
- Simulation and real data demonstrate practical effectiveness.

## Abstract

In this paper, 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.