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
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Official URL: http://linkinghub.elsevier.com/retrieve/pii/004725...
Related URL: http://dx.doi.org/10.1016/0047-259X(88)90113-3
Abstract
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 |
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