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Strong Gaussian Approximations of Product-Limit and Quantile Processes for Strong Mixing and Censored Data |
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| Authors: | V Fakoor N Nakhaei Rad |
| Institution: | 1. Department of Statistics, Ordered and Spatial Data Center of Excellence , Ferdowsi University of Mashhad , Mashhad, Iran fakoor@math.um.ac.ir;3. Department of Statistics, Faculty of Sciences , Islamic Azad University, Mashhad Branch , Mashhad, Iran |
| Abstract: | 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. |
| Keywords: | Censored dependent data Kaplan–Meier estimator Kiefer process Law of the iterated logarithm α-Mixing Strong Gaussian approximation |