Some asymptotics for multimodality tests based on kernel density estimates (original) (raw)

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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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Authors and Affiliations

1. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, W-6900, Heidelberg, Federal Republic of Germany
   E. Mammen
2. Department of Statistics, University of North Carolina, 27514, Chapel Hill, NC, USA
   J. S. Marron
3. CSIRO Division of Mathematics and Statistics, 2071, Lindfield, N.S.W., Australia
   N. I. Fisher

Authors

1. E. Mammen
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2. J. S. Marron
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3. N. I. Fisher
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Mammen, E., Marron, J.S. & Fisher, N.I. Some asymptotics for multimodality tests based on kernel density estimates.Probab. Th. Rel. Fields 91, 115–132 (1992). https://doi.org/10.1007/BF01194493

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• Received: 24 October 1990
• Revised: 26 August 1991
• Issue Date: March 1992
• DOI: https://doi.org/10.1007/BF01194493

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