Browsing by Subject "Kernel density estimators"

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    Bivariate density estimation with randomly truncated data
    (Elsevier, 2000) Gürler, Ü.; Prewitt, K.
    In 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 Press
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    Variance of the bivariate density estimator for left truncated right censored data
    (Elsevier, 1999) Prewitt, K.; Gürler, Ü.
    In this study the variance of the bivariate kernel density estimators for the left truncated and right censored (LTRC) observations are considered. In LTRC models, the complete observation of the variable Y is prevented by the truncating variable T and the censoring variable C. Consequently, one observes the i.i.d, samples from the triplets (T,Z,delta) only if T less than or equal to Z, Z=min(Y, C) and delta is one if Z=Y and zero otherwise. Gurler and Prewitt (1997, submitted for publication) consider the estimation of the bivariate density function via nonparametric kernel methods and establish an i.i.d. representation of their estimators. Asymptotic variance of the i.i.d, part of their representation is developed in this paper. Application of the results are also discussed for the data-driven and the least-squares cross validation bandwidth choice procedures. (C) 1999 published by Elsevier Science B.V. All rights reserved.