JSM 2004 Online Program

Abstract #301296

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Activity Number:	22
Type:	Contributed
Date/Time:	Sunday, August 8, 2004 : 2:00 PM to 3:50 PM
Sponsor:	IMS
Abstract - #301296
Title:	Estimation of a CDF and Its Derivative
Author(s):	François Perron*+
Companies:	Université de Montréal
Address:	Département de math, Université de Montréal, Montréal, PQ, H3C 3J7, Canada
Keywords:	splines ; order statistics ; nonparametric ; CDF ; estimation ; Hoefdings bounds
Abstract:	We consider the problem of estimating a CDF F by an estimator G based on a sample of size n. As n increases, we want G to be smooth on the regions where F is absolutely continuous and we want to obtain uniform convergence as well. Our approach uses splines with m nodes and the nodes depends on the sample. We show that our results hold if m tends to infinity as n tends to infinity. When F is absolutely continuous we show that the derivative of G tends to the derivative of F almost surely if m and n/m tend to infinity as n tends to infinity. We give some applications.

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