Is the Selected Population the Best?—Location and Scale Parameter Cases

We observe X 1,…,X k , where X i has density f(x,θ i ) possessing monotone likelihood ratio. The best population corresponds to the largest θ i . We select the population corresponding to the largest X i . The goal is to attach the best possible p-value to the inference: the selected population has the uniquely largest θ i . Gutmann and Maymin (1987) considered the location parameter case and derived the supremum of the error probability by conditioning on S, the index of the largest X i . Using this conditioning approach, Kannan and Panchapakesan (2009) considered the problem for the gamma family. We consider here a unified approach to both the location and scale parameter cases, and obtain the supremum of the error probability without using conditioning.