SOME SHRINKAGE ESTIMATORS FOR ESTIMATING THE STANDARD DEVIATION AND ITS INVERSE FOR NORMAL PARENT

Housila P. Singh; Vankim Chander

Housila P. Singh School of Studies in Vikram University, Ujjain, MP, India 456010 , Vankim Chander SAHARA Arts and Management Academy, Lucknow, UP, India Statistics in Transition new series, vol. 10, 2009, 1, pages: 25-58 Published online: 1 July 2009

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ABSTRACT

Shrunken estimator has its importance in the small sample theory when appropriate prior information about the unknown parameter is supposed to be known. The present paper investigates classes of shrunken estimators for estimating standard deviation (σ) and its inverse (σ^-1) in the case of univariate normal parent. The need to study these parameters arises due to their importance to estimate different parametric functions such as Mean Deviation about Mean, Process Capability Index (C_p), Standard Deviation (σ), Standard Error of Mean, Coefficient of Variation (C.V) with known mean etc., using the prior information or guessed value of σ . Simulation studies confirm the high efficiency of the developed classes of shrunken estimators when compared with their usual unbiased estimators and minimum mean squared error (MMSE) estimators.

KEYWORDS

Bias, Gauss-Laguerre integration method, Mean Squared Error, Normal parent, Percent Relative Efficiency (PRE), Prior information.

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