SOME ASYMPTOTICS FOR MULTIMODALITY TESTS BASED ON KERNEL DENSITY ESTIMATES
成果类型：
Article
署名作者：
MAMMEN, E; MARRON, JS; FISHER, NI
署名单位：
Commonwealth Scientific & Industrial Research Organisation (CSIRO); University of North Carolina; University of North Carolina Chapel Hill
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/BF01194493
发表日期：
1992
页码：
115-132
关键词：
摘要：
A test due to B.W. Silverman for modality of a probability density is based on counting modes of a kernel density estimator, and the idea of critical smoothing. An asymptotic formula is given for the expected number of modes. This, together with other methods, establishes the rate of convergence of the critically smoothed bandwidth. These ideas are extended to provide insight concerning the behaviour of the test based on bootstrap critical values.
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