SOME IMPROVED SHRINKAGE TESTIMATORS FOR VARIANCE OF NORMAL DISTRIBUTION UNDER ASYMMETRIC LOSS FUNCTION

Rakesh  Srivastava; Tejal  Shah

Rakesh Srivastava Department of Statistics, The M.S. University of Baroda, Vadodara, India
Tejal Shah Centre for Management Studies Ganpat University

Keywords: Normal Distribution, Variance, Shrinkage Testimator(s), Asymmetric Loss Function, Degrees of Asymmetry, Level of Significance, Relative Risk

Abstract

The present paper proposes some improved shrinkage testimator(s) for the variance of a normal distribution in presence of a guess value on it. Risk properties of these have been studied under an asymmetric loss function. It has been observed that proposed testimators perform better than the conventional estimators over a fairly large range of guess value to parameter ratio. The arbitrariness in the choice of shrinkage factor has been removed by making it dependent on test statistic. We have also considered the square of shrinkage factor as a different choice of shrinkage factor and it is observed that estimator proposed using this choice performs better than the other estimators. Recommendation on the degree(s) of asymmetry and level of significance has been made.

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