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

Science China Mathematics - Tập 44 - Trang 474-483 - 2001
Lincheng Zhao1, Chengqing Wu1
1Department of Statistics and Finance, University of Science and Technology of China, Heifei, China

Tóm tắt

LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+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.

Tài liệu tham khảo

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