On the asymptotic normality for integrated square error of Wegman-Davies recursive density estimators - Miao, Yu; Ye, Jun (Communications in statistics. Theory and methods, 2025)
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 } 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.