Iterative Distributed Multinomial Regression

TL;DR

This paper presents an iterative distributed estimator for multinomial logistic regression that is faster and asymptotically efficient, with a bootstrap inference procedure, validated through simulations.

Contribution

It introduces a novel iterative distributed estimator for multinomial logistic regression with improved speed and efficiency, along with a consistent bootstrap inference method.

Findings

Faster computation compared to maximum likelihood estimator

Achieves asymptotic efficiency with proper initialization

Validated through extensive simulation studies

Abstract

This article introduces an iterative distributed computing estimator for the multinomial logistic regression model with large choice sets. Compared to the maximum likelihood estimator, the proposed iterative distributed estimator achieves significantly faster computation and, when initialized with a consistent estimator, attains asymptotic efficiency under a weak dominance condition. Additionally, we propose a parametric bootstrap inference procedure based on the iterative distributed estimator and establish its consistency. Extensive simulation studies validate the effectiveness of the proposed methods and highlight the computational efficiency of the iterative distributed estimator.