Complete consistency and convergence rate of the nearest neighbor estimator of the density function based on WOD samples

Kan Chen, Xu ei Tang, Jiangf ng Hao

Type: Article

Publication Date: 2021-01-01

Citations: 0

DOI: https://doi.org/10.7153/jmi-2021-15-30

Abstract

By using the exponential inequality of widely orthant dependent (WOD, for short) random variables, we mainly investigate the complete consistency and convergence rate of the nearest neighbor estimator of the density function based on WOD samples.The results obtained in the paper generalize and improve some corresponding ones in the literature.In addition, the restriction on the dominating coefficients g(n) is much weak, even if the geometric growth of g(n) , the consistency result and convergence rate still hold by using the results that we obtained.

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Journal of Mathematical Inequalities - View - PDF

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Works Cited by This (21)

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+ PDF Chat	Negative Association of Random Variables with Applications	1983	Kumar Joag‐Dev Frank Proschan
+ PDF Chat	Uniform Consistency of Some Estimates of a Density Function	1969	David S. Moore Ernest G. Henrichon
+	Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables	2012	Wei He Dongya Cheng Yuebao Wang
+	The consistency of the nearest neighbor estimator of the density function based on WOD samples	2015	Xuejun Wang Shuhe Hu
+ PDF Chat	The Strong Uniform Consistency of Nearest Neighbor Density Estimates	1977	Luc Devroye T. Wagner
+	Basic renewal theorems for random walks with widely dependent increments	2011	Yuebao Wang Dongya Cheng
+	Precise large deviations for dependent random variables with heavy tails	2009	Li Liu
+ PDF Chat	A Nonparametric Estimate of a Multivariate Density Function	1965	D. O. Loftsgaarden Charles P. Quesenberry
+	Consistency of a nonparametric estimate of a density function for dependent variables	1988	Graciela Boente Ricardo Fraiman
+	On asymptotic approximation of inverse moments for a class of nonnegative random variables	2013	Aiting Shen