Gürler, Ü.Prewitt, K.2015-07-282015-07-2820000047-259Xhttp://hdl.handle.net/11693/11135In this study bivariate kernel density estimators are considered when a component is subject to random truncation. In bivariate truncation models one observes the i.i.d. samples from the triplets (T, Y, X) only if T less than or equal to 1: In this set-up, Y is said to be left truncated by T and T is right truncated by Y. We consider the estimation of the bivariate density function of (Y, X) via nonparametric kernel methods where Y is the variable of interest and X a covariate. We establish an i.i.d, representation of the bivariate distribution function estimator and show that the remainder term achieves an improved order of O(n(-1) In n), which is desirable fur density estimation purposes. Expressions are then provided for the bias and the variance of the estimators. Finally some simulation results are presented. (C) 2000 Academic PressEnglishBivariate distributionTruncation/censoringKernel density estimatorsArticle10.1006/jmva.1999.1875