Iterative stochastic restricted $r-d$ class estimator in generalized linear models: application to binomial, Poisson and negative binomial distributions

Year 2024, Volume: 53 Issue: 5, 1419 - 1437, 15.10.2024

Atıf Abbası , Revan Özkale

https://doi.org/10.15672/hujms.1261283

Abstract

In this paper, we provide an iterative stochastic restricted $r-d$ (SR-rd) class estimator that incorporates prior and sample information to address the multicollinearity problem. The newly proposed estimator is a manifold estimator that contains various estimators under specific conditions. The new estimator is compared to the maximum likelihood, principal components regression, and $r-d$ class estimators. To assess the performance, two numerical examples and two simulation studies are performed where the scalar mean square error and expected mean square error are the performance evaluation criteria. The analysis results show that the value of $d$ affects the performance of the estimators. The farther the $d$ value is from zero, the better the SR-rd estimator is compared to other estimators, and the SR-rd estimator is a good estimator at the optimal $d$ value.

Keywords

Stochastic restrictions; shrinkage parameter, mean square error, binomial distribution, Poisson distribution, negative binomial distribution, r-d class estimator

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