Strong Gaussian Approximations of Product-Limit and Quantile Processes for Strong Mixing and Censored Data

In this article, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian appr...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2010-01, Vol.39 (12), p.2271-2279
Main Authors: Fakoor, V., Rad, N. Nakhaei
Format: Article
Language:English
Subjects:
Approximation
Censored dependent data
Exact sciences and technology
Gaussian
General topics
Global analysis, analysis on manifolds
Kaplan-Meier estimator
Kiefer process
Law of the iterated logarithm
Mathematics
Nonparametric inference
Probability and statistics
Quantiles
Sciences and techniques of general use
Statistics
Strong Gaussian approximation
Studies
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
α-Mixing
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Summary:In this article, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and product-limit quantile process are constructed with rate O[(log n) −λ ] for some λ > 0. The strong Gaussian approximation of the product-limit process is then applied to derive the laws of the iterated logarithm for product-limit process.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610920903020779