Two approaches to grouping of data and related disparity statistics

Abstract

Csiszar's phi-divergences of discrete distributions are extended to a more general class of disparity measures by restricting the convexity of functions phi(t), t > 0, to the local convexity at t = 1 and monotonicity on intervals (0, 1) and (1, infinity). Goodness-of-fit estimation and testing procedures based on the phi-disparity statistics are introduced. Robustness of the estimation procedure is discussed and the asymptotic distributions for the testing procedure are established in statistical models with data grouped according to their values or orders.