New classes of estimators for dispersion parameter of a chi-distributed radial error with application to target analysis

Abstract

In this paper we have investigated some classes of shrinkage estimators for estimating dispersion parameter σ in p-dimensional analogue of the probable error of a single variate. The need to study this parameter arises due to its importance in target analysis problems to estimate Circular Probable Error (CPE) and Spherical Probable Error (SPE). It is assumed that the prior information or guessed value of the parameter σ say $σ_{0}$ is available from the past experiences. The properties of the developed shrinkage estimators have been studied when center of impact is known and when it is unknown by using appropriate numerical integration method (10-point Gauss-Laguerre integration method). Simulation studies confirm the high efficiency of the developed classes of shrunken estimators when compared with the usual maximum likelihood estimators (MLE), unbiased estimators and minimum mean squared error (MMSE) estimators.

Keywords

Bias Circular Probable Error (CPE)Gauss-Laguerre integration method Mean Squared Error (MSE)radial error Percent Relative Efficiency (PRE)prior information and Spherical Probable Error (SPE)