By Sheldon Ross

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Sample text

These probabilities can be calculated using the probability content of sectors of the bivariate normal. A simpler geometric approach has been described by Farebrother (1986) and is given below. 2 that the three stores are located at the same distance from the town square. One is in the direction N 30° E; the other at N 45° W; and the third located due S. 5°. 3958 3 Based on these calculations, a larger proportion of the population in Pitmanville will live closer to the location of store 3 than to the location of the two competing stores.

Which illustrates the presence of the Stein effect in the univariate case. Thus the sanctuary afforded by the Hodges-Lehmann landmark admissibility result for the sample mean does not extend to the criterion of PMC. 12) is known as a shrinkage factor since 0% shrinks X toward zero. The Efron estimator #2(X) is not unique in that A n (X) may 14 PITMAN'S MEASURE OF CLOSENESS be defined in many ways so that &i(X) is inadmissible to the associated estimator O^X) in the PMC sense. This form of inadmissibility was also presented by Salem and David in 1973.

3. In 1944 Geary made a significant contribution in the determination of the closeness probability for unbiased estimators of a common mean. 2. 8). The asymptotic nature of Geary's example prompted Scheffe (1945) to advocate the Pitman closeness criterion as a procedure for discrimination among consistent estimators of a common parameter. 2 and has connections with Rao's (1961) concept of second-order efficiency. The formal investigation of the asymptotic nature of the Pitman closeness criterion was started by Sen (1986a) with his study of best asymptotic normal (BAN) estimators.