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Moderate Deviation and Large Deviation for Wegman-Davies Recursive Density Estimators

Miao Yu, Gao Qinghui, Mu Jianyong, Deng Conghui

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 1

83--95

Let {Xk, k ≥ 1} be a sequence of independent identically distributed random variables with common probability density function f, and let fn denote a Wegman-Davies recursive density estimator [formula] where K is a kernel function and hn is a band sequence. In the prezent paper, the moderate deviation principle and the large deviation principle for the estimator fn are established.