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

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...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 54; no. 5; pp. 1328 - 1353
Main Authors Miao, Yu, Ye, Jun
Format Journal Article
LanguageEnglish
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
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Summary: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.
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content type line 14
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2024.2334803