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