ADAPTIVE SMOOTHING AND DENSITY-BASED TESTS OF MULTIVARIATE NORMALITY

• 成果类型: Article
• 署名作者: BOWMAN, AW; FOSTER, PJ
• 署名单位: University of Manchester
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2290333
• 发表日期: 1993
• 页码: 529-537
• 关键词: estimators

摘要

Methods of adaptive smoothing of density estimates, where the amount of smoothing applied varies according to local features of the underlying density, are investigated. The difficulties of applying Taylor series arguments in this context are explored. Simple properties of the estimates are investigated by numerical integration and compared with the fixed kernel approach. Optimal smoothing strategies, based on the multivariate Normal distribution, are derived. As an application of these techniques; two tests of multivariate Normality-one based on integrated squared error and one on entropy-are developed, and some power calculations are carried out.