Semiparametric Maximum Profile Likelihood Estimation of Polytomous and Sequential Choice Models

Abstract

This article considers semiparametric estimation of discrete choice models. The estimation methods are some semiparametric maximum profile likelihood methods which generalize Klein and Spady [1987] to the estimation of polytomous choice and sequential choice models. Special emphases are on the correction of asymptotic bias and negative density estimates caused by high order kernel density estimation. The estimators are shown to be Vn consistent and asymptotically normal. They attain the asymptotic efficiency bound of semiparametric estimation with some infinite dimensional parameter spaces of index probability functions.