Variable Selection via SCAD-Penalized Quantile Regression for High-Dimensional Count Data

Dost Muhammad Khan,Zardad Khan,Nadeem Iqbal,Mohd Amiruddin Abd Rahman,Mohd Shafie Mustafa,Mukhtaj Khan,Umair Khalil,Abdul Wahid,Anum Yaqoob

doi:10.1109/access.2019.2948278

Abstract

This article introduces a quantile penalized regression technique for variable selection and estimation of conditional quantiles of counts in sparse high-dimensional models. The direct estimation and variable selection of the quantile regression is not feasible due to the discreteness of the count data and non-differentiability of the objective function, therefore, some smoothness must be artificially imposed on the problem. To achieve the necessary smoothness, we use the Jittering process by adding a uniformly distributed noise to the response count variable. The proposed method is compared with the existing penalized regression methods in terms of prediction accuracy and variable selection. We compare the proposed approach in zero-inflated count data regression models and in the presence of outliers. The performance and implementation of the proposed method are illustrated by detailed simulation studies and real data applications.

Highlights

High-dimensional data are frequently collected in a large variety of research areas such as genomics, functional magnetic resonance imaging, tomography, economics and finance
Regularized regression techniques are important variable selection techniques based on the idea of penalized objective function that perform variable selection and coefficient estimation simultaneously
Hossain and Ahmed [17] studied the performance of Least Absolute shrinkage and selection operator (Lasso), adaptive Lasso and smoothly clipped absolute deviation (SCAD) penalties in Poisson regression model for both low and high dimensional data

Summary

INTRODUCTION

High-dimensional data are frequently collected in a large variety of research areas such as genomics, functional magnetic resonance imaging, tomography, economics and finance. Hossain and Ahmed [17] studied the performance of Lasso, adaptive Lasso and SCAD penalties in Poisson regression model for both low and high dimensional data. Since these are non-robust procedures, there is still the need of further studies on the implementation of penalized techniques for modeling count data. We will study the quantile regression of Machado and Silva [16] for count data with the SCAD penalty for variable selection, parameters estimation and as a remedy for a heavy-tailed distribution or outliers in the response.

QUANTILE REGRESSION FOR COUNT DATA

SELECTION OF TUNING PARAMETERS

SIMULATION STUDIES

REGULARIZED REGRESSION MODELS FOR ZERO-INFLATED COUNT DATA

Findings

CONCULUSION