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In statistical estimation procedure prior information regarding the unknown value of parameter is utilizing and it may result in a decrease of sampling variability of the estimator or it may save sample size which is desirable in many estimation procedures. The commonly used approaches in statistical inference which utilize prior information are Bayesian approach, preliminary test procedure and shrinkage estimation. The paper proposes preliminary test estimator and shrinkage preliminary test estimator for the variance in normal distribution and studies its property under Linex loss function. The paper also proposes and suggests shrinkage preliminary test estimator for the variance in negative exponential distribution and studies its property under Linex loss function.

Preliminary Test Estimation and Shrinkage Preliminary Test Estimation in Normal and Negative Exponential Distribution Using Linex Loss Function