A two stage shrinkage testimator for the mean of an exponential distribution
Let X be a random variable having an exponential distribution with unknown mean θ. Further, it is assumed that prior knowledge about θ is available in the form of an initial estimate θ00 of θ. It is proposed to estimate θ by a testimator that is based upon the result of a test of the hypothesis H0: θ = θ0. If H0 is accepted based on the first sample of size n1 we take where the weighting factor l is a function of the test statistic for testing H0. However, if H0 is rejected we obtain a second sample of size n2, and take . Choosing the weighing factor l appropriately, an expression for the mean squared error of is derived and comparisons are made with the variance of a single sample mean. Also an expression for the bias of is derived.