Penalized regression with multiple loss functions and selection by vote
Abstract
This article considers a linear model in a high dimensional data scenario. We propose a process which uses multiple loss functions both to select relevant predictors and to estimate parameters, and study its asymptotic properties. Variable selection is conducted by a procedure called "vote", which aggregates results from penalized loss functions. Using multiple objective functions separately simplifies algorithms and allows parallel computing, which is convenient and fast. As a special example we consider a quantile regression model, which optimally combines multiple quantile levels. We show that the resulting estimators for the parameter vector are asymptotically efficient. Simulations and a data application confirm the three main advantages of our approach: (a) reducing the false discovery rate of variable selection; (b) improving the quality of parameter estimation; (c) increasing the efficiency of computation.
Cite
@article{arxiv.2006.16361,
title = {Penalized regression with multiple loss functions and selection by vote},
author = {Guorong Dai and Ursula U. Müller},
journal= {arXiv preprint arXiv:2006.16361},
year = {2020}
}