Stein-type shrinkage estimators in gamma regression model with application to prostate cancer data

Abstract

Gamma regression is applied in several areas such as life testing, forecasting cancer incidences, genomics, rainfall prediction, experimental designs, and quality control. Gamma regression models allow for a monotone and no constant hazard in survival models. Owing to the broad applicability of gamma regression, we propose some novel and improved methods to estimate the coefficients of gamma regression model. We combine the unrestricted maximum likelihood (ML) estimators and the estimators that are restricted by linear hypothesis, and we present Stein-type shrinkage estimators (SEs). We then develop an asymptotic theory for SEs and obtain their asymptotic quadratic risks. In addition, we conduct Monte Carlo simulations to study the performance of the estimators in terms of their simulated relative efficiencies. It is evident from our studies that the proposed SEs outperform the usual ML estimators. Furthermore, some tabular and graphical representations are given as proofs of our assertions. This study is finally ended by appraising the performance of our estimators for a real prostate cancer data.

Keywords

asymptotic quadratic risk; gamma regression; positive-part Stein-type shrinkage estimator; prostate cancer; relative efficiency; Stein-type shrinkage estimator

Published in

Statistics in Medicine
2019, volume: 38, number: 22, pages: 4310-4322
Publisher: WILEY

SLU Authors

• Belaghi, Reza

  • University of Tabriz

UKÄ Subject classification

Probability Theory and Statistics

Publication identifier

• DOI: https://doi.org/10.1002/sim.8297

Permanent link to this page (URI)

https://res.slu.se/id/publ/126936