Pointwise Sharp Moderate Deviations for a Kernel Density Estimator

Siyu Liu, Xiequan Fan (), Haijuan Hu and Paul Doukhan
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Siyu Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Xiequan Fan: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Haijuan Hu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Paul Doukhan: CY University, AGM UMR 8088, Saint-Martin, 95000 Cergy-Pontoise, France

Mathematics, 2024, vol. 12, issue 20, 1-9

Abstract: Let f n be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random vectors taking values in R d . With some mild conditions, we establish sharp moderate deviations for the kernel density estimator. This means that we provide an equivalent for the tail probabilities of this estimator.

Keywords: Cramér moderate deviations; kernel density estimator; kernel function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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