Nonparametric regression estimators for length biased data

Ordinary kernel regression is not satisfactory when applied to length biased data sampling. In this paper, we propose several estimators of the regression function by way of modified local polynomials, and study their asymptotic optimal bandwidth and asymptotic mean squared error. We also analyze the situation where we have two types of samples, the first with length biased data and the second obtained directly from the population: in such cases, we calculate the asymptotic bias and variance of the resulting estimators under three alternative approaches. Finally, a simulation is carried out to compare the behavior of these estimators with finite samples. (C) 2000 Elsevier Science B.V. All rights reserved.