Inference for ordered parameters in multinomial distributions |
| |
Authors: | ShiFeng Xiong GuoYing Li |
| |
Affiliation: | (1) Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100190, China |
| |
Abstract: | This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions of their maximum likelihood estimators (MLEs) are not always normal and the bootstrap distribution estimators of the MLEs can be inconsistent. Then a class of weighted sum estimators (WSEs) of the ordered parameters is proposed. Properties of the WSEs are studied, including their asymptotic normality. Based on those results, large sample inferences for smooth functions of the ordered parameters can be made. Especially, the confidence intervals of the maximum cell probabilities are constructed. Simulation results indicate that this interval estimation performs much better than the bootstrap approaches in the literature. Finally, the above results for ordered parameters of multinomial distributions are extended to more general distribution models. This work was supported by National Natural Science Foundation of China (Grant No. 10371126) |
| |
Keywords: | multinomial distribution ordered parameters weighted sum estimator asymptotic normality |
本文献已被 SpringerLink 等数据库收录! |
|