Minimum phi-divergence estimators with constraints in multinomial populations

Abstract

This paper presents a minimum phi-divergence estimation procedure in multinomial models in which the probabilities depend on unknown parameters that are not mathematically independent but satisfy some functional relationships, This estimator is then used in a phi-divergence statistic for solving the problem of goodness-of-fit when the unknown parameters in the probabilities are not mathematically independent. The asymptotic distribution of this family of statistics is obtained under the null and contiguous alternative hypotheses, The asymptotic distribution of residuals. when the parameters are estimated using the minimum phi-divergence estimator. is also obtained.