Remarks on the Pitman’s Efficiency of Goodness of Fit Tests Based on Grouped Data

Abstract

We consider the problem of testing the goodness of fit of a continuous distribution to a set of observations grouped into equal probability intervals. We are interested in a class of tests based on symmetric statistics, which are defined as the sum of a function of interval-frequencies. The effect of changing of the number of intervals on the Pitman efficiency for a family of contamination alternatives is studied. It is assumed that the number of intervals increases asymptotically as the number of observations grows.