Minimum Profile Hellinger Distance Estimation for Semiparametric Simple Linear Regression Model

Abstract

The linear regression model is the most fundamental and the most commonly used one for analyzing associations between explanatory variables and response variables. This paper focuses on a semiparametric linear regression model where the distribution of error term is assumed symmetric but otherwise completely unspecified. Under this model, we propose a robust estimator of the regression coefficient parameters using the minimum Hellinger distance technique. Specifically, we construct a minimum profile Hellinger distance estimator (MPHDE) for the semiparametric linear regression model. In theory, we first investigate the identifiability of the model under consideration and then establish the consistency of the proposed MPHDE. The finite-sample performance of the proposed estimator is examined via simulation studies and real data applications. Our numerical results show that the proposed MPHDE has good efficiency and simultaneously is very robust against outlying observations.