Mixture of Regression Models with Single-Index

TL;DR

This paper introduces a flexible semiparametric mixture regression model with a single-index that effectively incorporates multivariate predictors, achieves optimal convergence rates, and demonstrates strong empirical performance.

Contribution

The paper proposes a novel semiparametric mixture regression model with a single-index, allowing multivariate predictors in nonparametric parts and providing efficient estimation algorithms.

Findings

Nonparametric functions estimated with asymptotic accuracy as if parameters were known.

Index parameters estimated with parametric root n rate.

Simulation and NBA data application confirm model effectiveness.

Abstract

In this article, we propose a class of semiparametric mixture regression models with single-index. We argue that many recently proposed semiparametric/nonparametric mixture regression models can be considered special cases of the proposed model. However, unlike existing semiparametric mixture regression models, the new pro- posed model can easily incorporate multivariate predictors into the nonparametric components. Backfitting estimates and the corresponding algorithms have been proposed for to achieve the optimal convergence rate for both the parameters and the nonparametric functions. We show that nonparametric functions can be esti- mated with the same asymptotic accuracy as if the parameters were known and the index parameters can be estimated with the traditional parametric root n convergence rate. Simulation studies and an application of NBA data have been conducted to demonstrate the finite sample performance of the proposed models.