Distributed Iterative Hard Thresholding for Variable Selection in Tobit Models

TL;DR

This paper develops a distributed iterative hard thresholding algorithm for variable selection in high-dimensional Tobit models, achieving near-optimal convergence rates and superior prediction accuracy, especially in censored data scenarios.

Contribution

It introduces a novel distributed IHT method for Tobit models, with theoretical guarantees and practical effectiveness demonstrated through simulations and real data.

Findings

Estimator converges at near-minimax rate

Distributed method requires few communication rounds

Achieves superior prediction and variable selection accuracy

Abstract

While extensive research has been conducted on high-dimensional data and on regression with left-censored responses, simultaneously addressing these complexities remains challenging, with only a few proposed methods available. In this paper, we utilize the Iterative Hard Thresholding (IHT) algorithm on the Tobit model in such a setting. Theoretical analysis demonstrates that our estimator converges with a near-optimal minimax rate. Additionally, we extend the method to a distributed setting, requiring only a few rounds of communication while retaining the estimation rate of the centralized version. Simulation results show that the IHT algorithm for the Tobit model achieves superior accuracy in predictions and subset selection, with the distributed estimator closely matching that of the centralized estimator. When applied to high-dimensional left-censored HIV viral load data, our method also exhibits similar superiority.