A Simple Consistent Non-parametric Estimator for the Regression Function in a Truncated Sample
نویسنده
چکیده
Much recent work has focused on the estimation of regression functions in samples which are truncated or censored. Much of this work has focused on the estimation of a parametric regression function with an error distribution of unknown form. While these method relax a strong parametric assumption about which we seldom have a priori information, they still impose a strong parametric assumption on the regression equation (which is presumably the focus of the analysis). Here we take the other approach. An estimator is proposed for the problem of non-parametric regression when the sample is truncated above or below some known threshold of the dependent variable. We specify the error distribution up to a vector of parameters while estimating the regression function without assuming a parametric form. A simple \back t" estimator based on an initial kernel smooth is proposed. We establish consistency results for this estimator when the error distribution is known up to a nite parameter vector and satis es some regularity conditions. A small monte-carlo study is performed to ascertain the nite sample properties of the estimator. The estimator is found to perform well in our experiment: achieving reasonable average absolute errors relative to the maximum likelihood estimator| especially when truncation is severe.
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