摘要
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.
Let X1,…,Xn be iid observations of a random variable X with pr obab ility density function f(x) on the q-dimensional unit sphere Ωq I n Rq+1 ,q≥1. Let fn(x)=n-1 c(h)∑ni=1 K［(1-x′Xi)/ h2］be a kernel estimator of f(x). In this paper we establish a central limit theorem for integrated square error of fn under some mild conditions.
