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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 centra