Kernel estimators of density function of directional data

Z. D. Bai, C. Radhakrishna Rao and L. C. Zhao

Journal of Multivariate Analysis, 1988, vol. 27, issue 1, 24-39

Abstract: Let X be a unit vector random variable taking values on a k-dimensional sphere [Omega] with probability density function f(x). The problem considered is one of estimating f(x) based on n independent observation X1,...,Xn on X. The proposed estimator is of the form fn(x) = (nhk-1)-1C(h) [Sigma]i=1n K[(1-x'Xi)/h2], x [set membership, variant] [Omega], where K is a kernel function defined on R+. Conditions are imposed on K and f to prove pointwise strong consistency, uniform strong consistency, and strong L1-norm consistency of fn as an estimator of f.

Keywords: directional; data; kernel; estimate; L1-norm; consistency; nonparametric; density; estimation; strong; consistency; uniform; consistency (search for similar items in EconPapers)
Date: 1988
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Citations: View citations in EconPapers (19)

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