Neyman's Smooth Goodness-of-Fit Test When the Hypothesis is Composite

Abstract

Abstract A method is given for adjustment of the Neyman smooth goodness-of-fit test to allow for estimation of parameters in a composite hypothesis. With this method the limiting distribution under the hypothesis is chi-squared, in contrast to a method given by Barton for this problem. The basis of the method is a standard modification of the quadratic score statistic. Key Words: Composite hypothesesGoodness of fitScore testsSmooth testsTest of normality