Strong Gaussian Approximations of Product-limit and Quantile Processes for Strong Mixing and Censored Data
نویسنده
چکیده
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)) 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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