Abstract
Motivated by recent work of Joe (1989, Ann. Inst. Statist. Math., 41, 683-697), we introduce estimators of entropy and describe their properties. We study the effects of tail behaviour, distribution smoothness and dimensionality on convergence properties. In particular, we argue that root-n consistency of entropy estimation requires appropriate assumptions about each of these three features. Our estimators are different from Joe's, and may be computed without numerical integration, but it can be shown that the same interaction of tail behaviour, smoothness and dimensionality also determines the convergence rate of Joe's estimator. We study both histogram and kernel estimators of entropy, and in each case suggest empirical methods for choosing the smoothing parameter.
Original language | English (US) |
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Pages (from-to) | 69-88 |
Number of pages | 20 |
Journal | Annals of the Institute of Statistical Mathematics |
Volume | 45 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1993 |
Externally published | Yes |
Keywords
- Convergence rates
- density estimation
- entropy
- histogram estimator
- kernel estimator
- projection pursuit
- root-n consistency
ASJC Scopus subject areas
- Statistics and Probability