Nonparametric Regression with Left-Truncated and Right-Censored Data

Abstract

Nonparametric regression is considered for left-truncated and right-censored (l.t.r.c.) data. An estimator of the regression function is developed when censoring and truncation are independent of covariates and the response. We develop an estimation procedure based on the product-limit estimator of the response variable and show how to apply nonparametric algorithms such as multivariate regression splines to l.t.r.c. data. We also illustrate nonparametric methods with a simulated data set and the Stanford heart transplant data. Under certain conditions, the L2 rate of convergence of the estimated regression function is obtained when tensor-produt of B-splines are used.