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

Authors:	ZHAO Lincheng WU Chengqing

Institution:	Department of Statistics and Finance, University of Science and Technology of China,

Abstract:	LetX ₁,…,X _n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ω_q in R^q+1,q ⩾ 1. Let $f_n (x) = n^{ - 1} c(h)\sum\nolimits_{i = 1}^n {K(1 - x'X_i )/h^2 ]}$ be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off _n under some mild conditions.

Keywords:	central limit theorem directional data kernel estimate integrated square error
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