Simulation and analytical approach to the identification of significant factors

TL;DR

This paper presents a new method combining simulation and analytical techniques to identify significant factors influencing non-binary response variables, with proven statistical properties and demonstrated efficiency through simulations.

Contribution

It introduces a novel approach for identifying significant factors in non-binary responses, including a new central limit theorem for regularized estimates.

Findings

Efficient identification of significant factors demonstrated via simulations

Proved a new central limit theorem for regularized estimates

Method applicable to biological and medical data

Abstract

We develop our previous works concerning the identification of the collection of significant factors determining some, in general, non-binary random response variable. Such identification is important, e.g., in biological and medical studies. Our approach is to examine the quality of response variable prediction by functions in (certain part of) the factors. The prediction error estimation requires some cross-validation procedure, certain prediction algorithm and estimation of the penalty function. Using simulated data we demonstrate the efficiency of our method. We prove a new central limit theorem for introduced regularized estimates under some natural conditions for arrays of exchangeable random variables. Keywords: nonbinary random response; identification of significant factors; regularized estimates of prediction error; exchangeable random variables; central limit theorem.