Improved Power in Multinomial Goodness-of-fit Tests
Ayanendranath Basu, Surajit Ray, Chanseok Park, Srabashi Basu
The Pearson's chi-square and the log likelihood ratio chi-square statistics are fundamental tools in goodness-of- fit testing. Cressie and Read (1984) constructed a general family of divergences which includes both statistics as special cases. This family is indexed by a single parameter, and divergences at either end of the scale are more powerful against alternatives of one type while being rather poor against the opposite type. Here we present several new goodness-of-fit testing procedures which have reasonably high power at both kinds of alternatives. Graphical studies illustrate the advantages of the new methods.
Keywords: Disparities, empty cell penalty, goodness-of-fit,power divergence.