Preliminary testing derivatives of a linear unified estimator in the logistic regression model

TL;DR

This paper introduces new derivatives of the Liu estimator for logistic regression, aiming to improve parameter estimation in ill-conditioned models through various shrinkage and testing techniques, supported by numerical and real data analyses.

Contribution

It proposes several improved Liu-type estimators for logistic regression, including restricted, preliminary test, and Stein-type shrinkage versions, enhancing estimation accuracy.

Findings

New estimators outperform traditional methods in simulations

Numerical results demonstrate improved estimation accuracy

Real data example confirms practical effectiveness

Abstract

Recently, the well known Liu estimator (Liu, 1993) is attracted researcher's attention in regression parameter estimation for an ill conditioned linear model. It is also argued that imposing sub-space hypothesis restriction on parameters improves estimation by shrinking toward non-sample information. Chang (2015) proposed the almost unbiased Liu estimator (AULE) in the binary logistic regression. In this article, some improved unbiased Liu type estimators, namely, restricted AULE, preliminary test AULE, Stein-type shrinkage AULE and its positive part for estimating the regression parameters in the binary logistic regression model are proposed based on the work Chang (2015). The performances of the newly defined estimators are analysed through some numerical results. A real data example is also provided to support the findings.