Improving on Admissible Estimators Under Entropy Loss Function

Abstract Consider $k ~(\ge 2)$ independent populations $\Pi_1, \ldots,\Pi_k$, where each population $\Pi_i$ follows an exponential distribution with hazard rate ${\beta_i},$ ($i = 1,\ldots,k$). Let $X_{i1},\ldots, X_{in}$ represent a random sample of size $n$ drawn from the $i$th population $\Pi_i$, where $i = 1,\ldots,k.$ For each $i = 1,\ldots,k$, consider $X_i=\sum_{j=1}^nX_{ij}$. Based on a special case of Gupta's rule \cite{B6}, estimation of the hazard rate associated with the selected population is undertaken with respect to the entropy loss function. Several natural estimators of the hazard rate of the corresponding population are proposed. A natural estimator is proved to be minimax. Estimators improving upon the natural ones are obtained by using the method of differential inequalities. Additionally, simulations are performed to have a comparative study of the proposed estimators based on their risk values.\vspace{2mm}\noindent{\bf{Keywords:}} Hazard rate; Natural selection rule; Differential inequality; Entropy loss function; Brewster-Zidek technique. \vspace{0.2cm}\noindent{\bf AMS subject classification (2020):} 62F07 ({\bf Primary}), 62F10, 62F15 ({\bf Secondary}).