A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

数学物理学报(英文版) ›› 1992, Vol. 12 ›› Issue (4): 472-478.

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A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

洪圣岩¹, 陈规景¹, 孔繁超¹, 高集体²

1. Dept. of Math., Anhui Univ, Hefei 230039, China;
2. Dept. of Math., Univ. of Sci. & Tech., Hefei 230026, China

收稿日期:1990-11-18 出版日期:1992-12-25 发布日期:1992-12-25
基金资助:
Research supported by National Natural Science Foundation of China.

A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

Hong Shenyan¹, Chen Guijing¹, Kong Fanchao¹, Gao Jiti²

1. Dept. of Math., Anhui Univ, Hefei 230039, China;
2. Dept. of Math., Univ. of Sci. & Tech., Hefei 230026, China

Received:1990-11-18 Online:1992-12-25 Published:1992-12-25
Supported by:
Research supported by National Natural Science Foundation of China.

摘要/Abstract

摘要： Let X be a d-dimensional random vector with unknown density function f(z)=f(z₁,…, z_d), and let f_n be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f_n for general case of d ≥ 1, which gives the exact pointwise strong convergence rate of f_n.

洪圣岩, 陈规景, 孔繁超, 高集体. A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION[J]. 数学物理学报(英文版), 1992, 12(4): 472-478.

Hong Shenyan, Chen Guijing, Kong Fanchao, Gao Jiti. A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION[J]. Acta mathematica scientia,Series B, 1992, 12(4): 472-478.

A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

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