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MODERATE DEVIATIONS AND LARGE DEVIATIONS FOR A TEST OF SYMMETRY BASED ON KERNEL DENSITY ESTIMATOR
Authors:He Xiaoxia  Gao Fuqing
Institution:[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China [2]College of Sciences, Wuhan University of Science and Technology, Wuhan 430081, China
Abstract:Let fn be a non-parametric kernel density estimator based on a kernel function K. And a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup x∈R|fn(x) - fn(-X)|.
Keywords:Symmetry test  kernel estimator  moderate deviations  large deviations
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