Estimation of entropy and other functionals of a multivariate density

✍ Scribed by Harry Joe

• Publisher: Springer Japan
• Year: 1989
• Tongue: English
• Weight: 630 KB
• Volume: 41
• Category: Article
• ISSN: 0020-3157
• DOI: 10.1007/bf00057735

✦ Synopsis

For a multivariate densityfwith respect to Lebesgue measure /l, the estimation offJ(f)fdl~, and in particularff2dl~ and -ff log fdl~, is studied. These two particular functionals are important in a number of contexts. Asymptotic bias and variance terms are obtained for the estimators i =fJ(f)dF, and 7 --fJ(f)f d#, where f is a kernel density estimate off and F, is the empirical distribution function based on the random sample Xt,...,X, from f. For the two functionals mentioned above, a first order bias term for i can be made zero by appropriate choices of non-unimodal kernels. Suggestions for the choice of bandwidth are given; for ? =ffdF,, a study of optimal bandwidth is possible.