K phi divergence statistics in multinomial populations

Abstract

Asymptotic distributions of K-phi-divergence statistics are derived by either testing goodness-of-fit under symmetric null hypothesis, or composite null hypotheses when the unspecified parameters are estimated by minimum K-phi-divergence. The asymptotic chi-square null distribution and three alternative approximations to the exact distribution function of this family are considered and a new goodness-of fit statistics emerges as an alternative to Pearson's chi-square test. Test of homogeneity is also obtained.