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Biometrika 2004 91(1):113-123; doi:10.1093/biomet/91.1.113
© 2004 by Biometrika Trust
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Testing for multimodality with dependent data

K.S. Chan1 and H.Tong2

1 Department of Statistics & Actuarial Science, University of Iowa, Iowa City, Iowa 52242, U.S.A.kung-sik-chan{at}uiowa.edu 2 Department of Statistics & Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Konghtong{at}khustas1.hku.hk

We propose a test for multimodality with dependent data by resampling from a suitably constructed transition probability kernel, which includes Silverman's test with independent data as a special case.We extend some theoretical properties of Silverman's test with independent and identically distributed data to weakly dependent data, and also discuss the robustness of Silverman's test against departure from independence.

Key Words: Gaussian kernel; Markov chain; Silverman's test; Smoothed autoregressive bootstrap; Uniform ergodicity

Received May 2002. Revised April 2003


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