Inference for ordered parameters in multinomial distributions

摘要: This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions their maximum likelihood estimators (MLEs) are not always normal and bootstrap distribution MLEs can be inconsistent. Then a class weighted sum (WSEs) is proposed. Properties WSEs studied, including normality. Based on those results, large sample inferences smooth functions made. Especially, confidence intervals cell probabilities constructed. Simulation results indicate this interval estimation performs much better than approaches in literature. Finally, above extended to more general models.