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Estimating a distribution function with truncated data

Estimating a distribution function with truncated data Let (X i,Y i),i=1, 2,..., be i.i.d. vector valued random variables with unknown common marginal distribution functionsF(x) andG(x). One model of incomplete observations studied in the literature is the truncated model, where bothX i andY i are observed ifX i ≥Y i, and nothing can be observed otherwise. From this kind of observations, if any, we describe the modified nonparametric maximum likelihood estimators ofF(x). The law of the iterated logarithm for the uniform covergence is proved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Estimating a distribution function with truncated data

He, Shuyuan
Acta Mathematicae Applicatae Sinica , Volume 10 (1) – Jul 13, 2005
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References (6)

Publisher
Springer Journals
Copyright
Copyright © 1994 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006256
Publisher site
See Article on Publisher Site

Abstract

Let (X i,Y i),i=1, 2,..., be i.i.d. vector valued random variables with unknown common marginal distribution functionsF(x) andG(x). One model of incomplete observations studied in the literature is the truncated model, where bothX i andY i are observed ifX i ≥Y i, and nothing can be observed otherwise. From this kind of observations, if any, we describe the modified nonparametric maximum likelihood estimators ofF(x). The law of the iterated logarithm for the uniform covergence is proved.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 13, 2005

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