ADAPTIVE ESTIMATION STRATEGIES IN GAMMA REGRESSION MODEL
Assistant Professor Dr. SUPRANEE LISAWADI DEPARTMENT OF MATHEMATICS AND STATISTICS
The goal of this study was to address the parameter estimation problem in the gamma
regression when the available subspace information was uncertain and the problems of over-fitting and under-fitting occurred. we present the pretest and shrinkage estimation strategies, providing the highly effective in parameter estimation and overcoming the performance of classical MLE.
Both theoretically and from numerical studies, as we expect, the use of full model lead to the over-fitting problem and the performance of the MLE-based full model estimator became very poor when the true subspace information was available. Consequently, this estimator is not recommended for parameter estimation in the gamma regression model. We can address the problem of over-fitting in gamma regression models by using MLEbased submodel estimation when the available subspace information was not true. However, its efficiency is less than that of all other estimators when the subspace information becomes invalid. Hence, the use of the MLE-based submodel estimator, introducing under-fitting problem, is not suggested in that case.
The proposed estimators were shown to produce more efficient parameter estimates
than the classical MLE-based full model or submodel estimators, which may provide over-fitting and under-fitting, respectively. For small values of q, the pretest-based estimators
performed well when the subspace information was true or nearly true. The three versions of the shrinkage estimator, especially in their truncated versions, produced superior estimates, regardless of the accuracy of the subspace information. We observed that the shrinkage estimators using were the most robust of the versions investigated.
Finally, the predictive performance of the proposed estimators was studied using a real application. The results confirmed the theoretical and numerical findings. Therefore, it would be safe to use the shrinkage estimator using for dealing with the presence of uncertain subspace information. Nevertheless, this estimator has the condition that the number of inactive covarites must be greater than or equal to three (q _ 3). Therefore, the shrinkage pretest estimator is recommended to used when the number of inactive covarites is less than three (q < 3).