Limit theorems for nonparametric sample entropy estimators

Statistics and Probability Letters

Volumn 49, Issue 1, 2000, Pages 9-18

  Song, Kai Sheng ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Consistency; Entropy central limit theorem; Heavy tails* m spacings; Nonparametric density estimation; Order statistics; Shannon entropy; Vasicek sample entropy

Indexed keywords

EID: 0043280948     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(00)00025-0     Document Type: Article

References (9)

1. Ahmad I.A., Lin P.E. A nonparametric estimation of the entropy for absolutely continuous distributions. IEEE Trans. Inform. Theory. 22:1976;372-375.
2. Bloch D.A., Gastwirth J.L. On a simple estimate of the reciprocal of the density function. Ann. Math. Statist. 39:1968;1083-1085.
3. Dmitriev Y.G., Tarasenko F.P. On the estimation of functional of the probability density and its derivatives. Theory Probab. Appl. 18:1973;628-633.
4. Mack, S., 1988. A comparative study of entropy estimators and entropy-based goodness-of-fit tests, Ph.D. Dissertation, University of California, Riverside.
5. Rao C.R. Linear Statistical Inference and Its Applications. 1973;Wiley, New York.
6. Rao, C.R., Zhao, L.C., 1997. A limiting distribution theorem. Festschrift for Lucien Le Cam. Springer, Berlin, pp. 325-335.
7. Siddiqui M.M. Distribution of quantiles in samples from a bivariate population. J. Res. Natl. Bur. Stand. B. 64:1960;145-150.
8. Vasicek O. A test for normality based on sample entropy. J. Roy. Statist. Soc. B. 38:1976;54-59.
9. Zhu L.X., Wong H.L., Fang K.-T. A test for multivariate normality based on sample entropy and projection pursuit. J. Statist. Plann. Inference. 45:1995;373-385.