Kernel estimators of density function of directional data

Bai, Z. D. ; Radhakrishna Rao, C. ; Zhao, L. C. (1988) Kernel estimators of density function of directional data Journal of Multivariate Analysis, 27 (1). pp. 24-39. ISSN 0047-259X

Full text not available from this repository.

Official URL:

Related URL:


Let X be a unit vector random variable taking values on a k-dimensional sphere Ω 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) Σi=1n K[(1-x'Xi)/h2], x εΩ, 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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Directional Data; Kernel Estimate; L1-norm Consistency; Nonparametric Density Estimation; Strong Consistency; Uniform Consistency
ID Code:42479
Deposited On:04 Jun 2011 08:52
Last Modified:04 Jun 2011 08:52

Repository Staff Only: item control page