On the estimation of entropy |
| |
Authors: | Peter Hall and Sally C Morton |
| |
Institution: | (1) Centre for Mathematics and its Applications, Australian National University, G.P.O. Box 4, 2601 Canberra, A.C.T., Australia;(2) CSIRO Division of Mathematics and Statistics, Australia;(3) Statistical Research and Consulting Group, The RAND Corporation, 1700 Main Street, P.O. Box 2138, 90407-2138 Santa Monica, CA, USA |
| |
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. |
| |
Keywords: | Convergence rates density estimation entropy histogram estimator kernel estimator projection pursuit root-n consistency |
本文献已被 SpringerLink 等数据库收录! |
|