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

• Published in: Statistics in medicine Vol. 38; no. 22; pp. 4310 - 4322
• Main Authors: Mandal, Saumen, Arabi Belaghi, Reza, Mahmoudi, Akram, Aminnejad, Minoo
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 30.09.2019
• Subjects: asymptotic quadratic risk; Computer Simulation; Economic models; gamma regression; Humans; Likelihood Functions; Male; Monte Carlo Method; positive-part Stein-type shrinkage estimator; Prostate cancer; Prostatic Neoplasms; Regression Analysis; relative efficiency; Stein-type shrinkage estimator; Survival Analysis; asymptotic quadratic risk; relative efficiency; prostate cancer; gamma regression; Stein-type shrinkage estimator; positive-part Stein-type shrinkage estimator
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.8297

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.