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arXiv · 2412.05620

Improved estimation of the positive powers ordered restricted standard deviation of two normal populations

Somnath Mondal·Lakshmi Kanta Patra
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Abstract

The present manuscript is concerned with component-wise estimation of the positive power of ordered restricted standard deviation of two normal populations with certain restrictions on the means. We propose several improved estimators under a general scale invariant bowl-shaped loss function. Also, we proposed a class of improved estimators. It has been shown that the boundary estimator of this class is a generalized Bayes. As an application, the improved estimators are obtained with respect to quadratic loss, entropy loss, and a symmetric loss function. We have conducted extensive Monte Carlo simulations to study and compare the risk performance of the proposed estimators. Finally, a real life data analysis is given to illustrate our findings.

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Somnath Mondal, Lakshmi Kanta Patra. 2024-12-07. Improved estimation of the positive powers ordered restricted standard deviation of two normal populations. https://arxiv.org/abs/2412.05620

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