Central limit theorem for integrated square error of kernel estimators of spherical density

被引：15

作者：

Zhao, LC ^{[1
]}

Wu, CQ ^{[1
]}

机构：

[1] Univ Sci & Technol China, Dept Stat & Finance, Hefei 230026, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY | 2001年 / 44卷 / 04期

关键词：

central limit theorem; directional data; kernel estimate; integrated square error;

D O I：

10.1007/BF02881884

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X,,,X, be lid observations of a random variable X with probability density function f(x) on the q-dimensional unit sphere Ohm (q), in Rq+1, q greater than or equal to 1. Let f(n)(x) = n(-1)c(h) Sigma K-n(i=1)[(1-x'X-i)/h(2)] be a kernel estimator of f(x). In this paper we establish a central limit theorem for integrated square error of f(n) under some mild conditions.

引用

页码：474 / 483

页数：10

共 36 条

[21] Central limit theorem for the heat kernel measure on the unitary group
Levy, Thierry
Maida, Mylene
JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (12) : 3163 - 3204
[22] A central limit theorem for the Hellinger loss of Grenander-type estimators
Lopuhaa, Hendrik P.
Musta, Eni
STATISTICA NEERLANDICA, 2019, 73 (02) : 180 - 196
[23] Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting
Brehier, Charles-Edouard
Goudenege, Ludovic
Tudela, Loic
MONTE CARLO AND QUASI-MONTE CARLO METHODS, 2016, 163 : 245 - 260
[24] Central limit theorems for the Lp-error of smooth isotonic estimators
Lopuhaa, Hendrik P.
Musta, Eni
ELECTRONIC JOURNAL OF STATISTICS, 2019, 13 (01): : 1031 - 1098
[25] On Estimation of the Approximation Error in Asymptotic Expansions in the Central Limit Theorem
V. V. Senatov
Journal of Mathematical Sciences, 2002, 112 (2) : 4174 - 4197
[26] AVERAGE ERROR IN THE CENTRAL-LIMIT-THEOREM FOR THE CUMULATIVE PROCESSES
ROGINSKY, A
STATISTICS & PROBABILITY LETTERS, 1995, 24 (03) : 199 - 204
[27] CENTRAL LIMIT THEOREM FOR MEAN AND VARIOGRAM ESTIMATORS IN LEVY-BASED MODELS
Ronn-Nielsen, Anders
Jensen, Eva B. Vedel
JOURNAL OF APPLIED PROBABILITY, 2019, 56 (01) : 209 - 222
[28] NONCLASSICAL ERROR BOUNDS FOR ASYMPTOTIC EXPANSIONS IN THE CENTRAL LIMIT THEOREM
Yaroslavtseva, L. S.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2009, 53 (02) : 365 - 367
[29] Exploring Central Limit Theorem on World Population Density Data
Fitrianto, Anwar
Hanafi, Imam
INTERNATIONAL CONFERENCE ON QUANTITATIVE SCIENCES AND ITS APPLICATIONS (ICOQSIA 2014), 2014, 1635 : 737 - 741
[30] Density estimates and central limit theorem for the functional of fractional SDEs
Nguyen Tien Dung
STOCHASTIC ANALYSIS AND APPLICATIONS, 2019, 37 (01) : 74 - 89

← 1 2 3 4 →