Strong Gaussian approximations of product-limit and Quantile Processes for Strong mixing and censored data

2008/12/16 by V. Fakoor, Fakoor, V., N. Nakhaee Rad +1
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.0812.3038

Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)

arxiv created 2008/12/16 · arxiv updated 2009/12/01

Abstract

In this paper, 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.

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