Most Stringent Test for Location Parameter of a Random Number from Cauchy Density

Abstract

We study the test for location parameter of a random number from Cauchy density, focusing on point optimal tests. We develop analytical technique to compute critical values and power curve of a point optimal test. We study the power properties of various point optimal tests. The problem turned out to be different in its nature, in that, the critical value of a test determines the power properties of test. We found that if for given size  and any point m in alternative space, if the critical value of a point optimal test is 1, the test optimal for that point is the most stringent test.Cauchy density, Power Envelop, Location Parameter, Stringent Test