Article A preliminary test single stage shrinkage (PTSSS)‎ techniques

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A preliminary test single stage Shrinkage (PTSSS) techniques is used for estimation the scale parameter q of an exponential distribution when a prior knowledge about q is a available in the form of initial estimate q0 of q.

It is proposed to estimate q by a testimator q% that is based upon the result of a test of the hypothesis H0 :q = q0 against the hypothesis HA :q ¹ q0 with level of significance a.

If H0 is accepted we take ˆ ˆ ) 1 0 0 q = y (q)(q − q + q % , where the weighting factor ˆ 1 y (q) is a function of the test statistic for testing H0 or may be constant such that 0 ˆ 1 £ y (q) £1.

However if H0 is rejected we take ˆ ˆ ) 2 0 0 q = y (q)(q − q + q % , where 0 ˆ 2 £ y (q) £1 and ˆq is the classical estimator of q (MLE).

Choosing the weighting factor i y (qˆ ) , (i =1,2) appropriately, an expression for the mean squared error (MSE) and Bias of q% are derived and comparisons are made with classical estimator (ˆq ) in the sense of efficiency and last earlier studies.