On the Limiting Power Function of the Frequency Chi-Square Test

in the usual manner, Cochran, in an expository article 10 has suggested the derivation of its Pitman limiting power 11, and he illustrated it in the case of the simple goodness of fit test. The colncept of asymptotic power suggested by Pitman has also been extensively used in various other areas like nonparametric inference (see e.g. Hoeffding and Rosenblatt 12) and seems to be a useful tool for comparing alternative consistent tests or alternative designs for experimentation, with regard to their performance in the immediate neighbourhood of the null hypothesis. The consistency of the frequency X2-test has already been established by Neyman 13. The object of the present paper is to obtain the Pitman limiting power of this test when the unknown parameters occurring in the specification of class probabilities are estimated from the sample by an asymptotically efficient method like the method of maximum likelihood, minimum x2 etc. In section 5, we discuss a few applications of the Pitman limiting power for frequency x2-tests.