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

• Published in: Communications in statistics. Theory and methods Vol. 54; no. 5; pp. 1328 - 1353
• Main Authors: Miao, Yu, Ye, Jun
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 04.03.2025; Taylor & Francis Ltd
• Subjects: Asymptotic methods; Asymptotic normality; Asymptotic properties; Estimators; integrated square error; Kernel functions; martingale; Martingales; Normality; Probability density functions; Random variables; recursive density estimators; Recursive functions

In this article, let { X n , n ≥ 1 } be a sequence of i.i.d. random variables with common probability density function f, and f ̂ n denotes a Wegman-Davies recursive density estimator f ̂ n ( x ) = 1 n h n 1 / 2 ∑ i = 1 n 1 h i 1 / 2 K ( x − X i h i ) , where K is a kernel function and { h i , i ≥ 1...