# Seminar by Dr. Lakshmi Kanta Patra

Speaker: Dr. Lakshmi Kanta Patra;
Date: 11th March, 2019 (Monday);
Time: 12 Noon;
Venue: Committee Room, Department of Mathematics.

Title: Estimating a function of scale parameter of an exponential
population with unknown location.

Abstract: We have considered the problem of estimating a function of scale parameter $\ln \simga$ of an exponential distribution under an arbitrary location invariant bowl-shaped loss function, when location parameter $\mu$ is unknown. Various improved estimators are proposed. Inadmissibility of the best affine equivariant estimator (BAEE) of
$\ln\sigma$ is established by deriving a Stein-type estimator. This improved estimator is not smooth. We derive a smooth estimator improving upon the BAEE. Further, the integral expression of risk difference (IERD) approach of Kubokawa is used to derive a class of improved estimators. To illustrate these results, we consider two specific loss functions: squared error and linex loss functions, and derive various estimators improving upon the BAEE. Finally, a simulation study has been carried out to numerically compare the risk performance of the improved estimators.