Levy, Armando: A Simple Consistent Non-parametric Estimator of the Regression Function in a Truncated Sample
World Conference Econometric Society, 2000, Seattle

Armando Levy, North Carolina State University
A Simple Consistent Non-parametric Estimator of the Regression Function in a Truncated Sample
Session: C-10-17  Tuesday 15 August 2000  by Levy, Armando
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 ``backfit'' 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 finite parameter vector and satisfies some regularity conditions. A small monte-carlo study is performed to ascertain the finite sample properties of the estimator. The estimator is found to perform well in our experiment: achieving reasonableaverage absolute errors relative to the maximum likelihood estimator- especially when truncation is severe.
Submitted paper full-text in .pdf


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