Hall [J. Multivariate Anal. 14 (1984) 1-16; Ann. Statist. 12 (1984) 241 260] established central limit theorems for the integrated square errors of multivariate nonparametric function estimators. In this article, we extend his results and derive central limit theorems for the averaged square errors
Limit theorems for nonparametric sample entropy estimators
β Scribed by Kai-Sheng Song
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 110 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
β¦ Synopsis
We obtain, for the ΓΏrst time in the literature, the central limit theorem for nonparametric sample entropy estimators in its full generality together with maximum likelihood entropy estimators. Also we provide a new proof of the consistency of the estimators to correct some problems in Vasicek's original proof as pointed out by Zhu et al. (J. Statist. Plann. Inference 45 (1995) 373-385).
π SIMILAR VOLUMES
Park et al. (Econometric Theory 16 (2000) 855) and Gijbels et al. (J. Amer. Statist. Assoc. 94 (1999) 220) derived the limit distributions of the two most popular nonparametric estimators, FDH and DEA, of a boundary in a setting where the density or intensity of the data has a sharp or fault-type b