On the asymptotic normality for integrated square error of Wegman-Davies recursive density estimators

Yu Miao and Jun Ye

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 5, 1328-1353

Abstract: In this article, let {Xn,n≥1} be a sequence of i.i.d. random variables with common probability density function f, and f̂n denotes a Wegman-Davies recursive density estimator f̂n(x)=1nhn1/2∑i=1n1hi1/2K(x−Xihi), where K is a kernel function and {hi,i≥1} is a sequence of band-width parameters. The asymptotic normality for integrated square error of Wegman-Davies recursive density estimators are established by using martingale method.

Date: 2025
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DOI: 10.1080/03610926.2024.2334803

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