Enhancing liu-type estimation for poisson-modified quasi-lindley regression

Abstract

This study develops an improved Liu‑type estimator for the Poisson‑modification of the quasi‑Lindley regression model (PMQL‑RM) to handle overdispersed count data in the presence of severe multicollinearity. We first formulate the PMQL‑RM and review existing shrinkage estimators, including the PMQL ridge estimator, the PMQL Liu estimator, and a previously proposed PMQL Liu‑type estimator. Building on recent work on improved Liu‑type estimators in generalized linear models, we introduce a new PMQL improved Liu‑type estimator (PMQL‑ILTE) that incorporates an eigenvalue‑dependent biasing function, yielding a flexible one‑parameter shrinkage scheme so that the shrinkage applied to each regression direction is tailored to the corresponding eigenvalue of the information matrix. We derive closed‑form expressions for the bias, variance–covariance matrix, matrix mean squared error (MMSE), and scalar MSE. A comprehensive Monte Carlo study is then conducted, varying multicollinearity levels, sample sizes, number of predictors, and dispersion parameters. The simulation results show that the PMQL‑ILTE uniformly achieves the smallest MSE across all scenarios, with especially pronounced gains under high multicollinearity and moderate‑to‑large samples. Finally, an application to Swedish football league data demonstrates the practical relevance of the proposed estimator. Relative to PMQL‑MLE and other shrinkage competitors, PMQL‑ILTE substantially reduces the estimated MSE while stabilizing regression coefficients without altering their signs or substantive ranking. Overall, the results indicate that the proposed estimator provides an efficient alternative for modeling overdispersed count responses with multicollinear covariates.