Mathematics – Statistics Theory
Scientific paper
2008-12-16
Mathematics
Statistics Theory
Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics
Scientific paper
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 $O((\log n)^{-\lambda})$ for some $\lambda>0,$. The strong Gaussian approximation of the product-limit process is then applied to derive the laws of the iterated logarithm for product-limit process.
Fakoor V.
Rad Nakhaee N.
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