A Strong Representation of the Product-Limit Estimator for Left Truncated and Right Censored Data
In this paper we consider the TJW product-limit estimatorFn(x) of an unknown distribution functionFwhen the data are subject to random left truncation and right censorship. An almost sure representation of PL-estimatorFn(x) is derived with an improved error bound under some weaker assumptions. We obtain the strong approximation ofFn(x)-F(x) by Gaussian processes and the functional law of the iterated logarithm is proved for maximal derivation of the product-limit estimator toF. A sharp rate of convergence theorem concerning the smoothed TJW product-limit estimator is obtained. Asymptotic properties of kernel estimators of density function based on TJW product-limit estimator is given.
Year of publication: |
1999
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Authors: | Zhou, Yong ; Yip, Paul S. F. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 69.1999, 2, p. 261-280
|
Publisher: |
Elsevier |
Keywords: | truncated data censored data product-limit estimator almost sure representation |
Saved in:
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