Iterative distributed multinomial regression

Abstract

This article introduces an iterative distributed computing (IDC) estimator for the multinomial logistic regression model with large choice sets. The IDC estimator reformulates the estimation problem as a sequence of structured, low-dimensional subproblems that can be solved efficiently and in parallel. We establish that, when initialized with a consistent estimator, the IDC estimator is asymptotically equivalent to the maximum likelihood estimator and achieves asymptotic efficiency under a weak dominance condition. We further develop a parametric bootstrap procedure for inference based on the IDC estimator and prove its consistency. Extensive simulation studies validate the effectiveness of the proposed methods and highlight the computational efficiency of the IDC estimator.