Inference in the Presence of Likelihood Monotonicity for Polytomous and Logistic Regression

作     者：John E. Kolassa John E. Kolassa

作者机构：Department of Statistics and Biostatistics Rutgers University Piscataway NJ USA 

出 版 物：《Advances in Pure Mathematics》 (理论数学进展（英文）)

年 卷 期：2016年第6卷第5期

页      面：331-341页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Polytomous Regression Likelihood Monotonicity Saddlepoint Approximation 

摘      要：This paper addresses the problem of inference for a multinomial regression model in the presence of likelihood monotonicity. This paper proposes translating the multinomial regression problem into a conditional logistic regression problem, using existing techniques to reduce this conditional logistic regression problem to one with fewer observations and fewer covariates, such that probabilities for the canonical sufficient statistic of interest, conditional on remaining sufficient statistics, are identical, and translating this conditional logistic regression problem back to the multinomial regression setting. This reduced multinomial regression problem does not exhibit monotonicity of its likelihood, and so conventional asymptotic techniques can be used.