2023/09/25 by Naresh Kumar Garg, Neeraj Misra, Garg, Naresh +1
Mathematics · #62C99 #62F10 #62F30 #FOS: Mathematics #G.3 #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST) #Survey Sampling and Estimation Techniques
paper · pdf · doi:10.48550/arxiv.2309.13880
openalex publication_date 2023/09/25 · openalex created_date 2023/09/27 · openalex updated_date 2026/07/28
The problem of simultaneous estimation of order restricted location parameters θ1 and θ2 (-∞<θ1≤ θ2<∞) of a bivariate location symmetric distribution, under a general loss function, is being considered. In the literature, many authors have studied this problem for specific probability models and specific loss functions. In this paper, we unify these results by considering a general bivariate symmetric model and a quite general loss function. We use the Stein and the Kubokawa (or IERD) techniques to derive improved estimators over any location equivariant estimator under a general loss function. We see that the improved Stein type estimator is robust with respect to the choice of a bivariate symmetric distribution and the loss function, as it only requires the loss function to satisfy some generic conditions. A simulation study is carried out to validate the findings of the paper. A real-life data analysis is also provided.