Asymptotic behavior of robust estimators in partially linear models with missing responses: The effect of estimating the missing probability on the simplified marginal estimators

Abstract

In this paper, we consider a semiparametric partially linear regression model where missing data occur in the response. We derive the asymptotic behavior of the robust estimators for the regression parameter and of the weighted simplified location estimator introduced in Bianco et al. (Comput. Stat. Data Anal. 54:546–564, 2010a). For the latter, consistency results and the asymptotic distribution are derived when the missing probability is known and also when it is estimated.