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- Title
Large deviations and moderate deviations for kernel density estimators of directional data.
- Authors
Fu Quing Gao; Li Na Li
- Abstract
Let f n be the non-parametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere S d−1. It is proved that if the kernel function is a function with bounded variation and the density function f of the random variables is continuous, then large deviation principle and moderate deviation principle for $$ \left\{ {\sup _{x \in S^{d - 1} } |f_n (x) - E(f_n (x))|,n \geqslant 1} \right\} $$ hold.
- Subjects
KERNEL functions; LARGE deviations (Mathematics); LIMIT theorems; RANDOM variables; MATHEMATICAL variables
- Publication
Acta Mathematica Sinica, 2010, Vol 26, Issue 5, p937
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-010-7205-9