Estimation of the Directions for Unknown Parameters in Semiparametric Models

TL;DR

This paper introduces a new least squares estimator for determining the direction of unknown parameters in semiparametric models, demonstrating consistency and superior performance over existing methods in simulations and real data.

Contribution

It proposes a novel estimator that is consistent, asymptotically distributed, and effective without knowing the link function form, improving estimation in semiparametric models.

Findings

Estimator outperforms maximum score estimator in simulations

Performs well with long-tailed error distributions

Successfully applied to export participation data in Guangdong

Abstract

Semiparametric models are useful in econometrics, social sciences and medicine application. In this paper, a new estimator based on least square methods is proposed to estimate the direction of unknown parameters in semi-parametric models. The proposed estimator is consistent and has asymptotic distribution under mild conditions without the knowledge of the form of link function. Simulations show that the proposed estimator is significantly superior to maximum score estimator given by Manski (1975) for binary response variables. When the error term is long-tailed distributions or distribution with infinity moments, the proposed estimator perform well. Its application is illustrated with data of exporting participation of manufactures in Guangdong.