Some asymptotics for multimodality tests based on kernel density estimates
SummaryA 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 converge...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
1992
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| In: |
Probability theory and related fields
Year: 1992, Jahrgang: 91, Heft: 1, Pages: 115-132 |
| ISSN: | 1432-2064 |
| DOI: | 10.1007/BF01194493 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1007/BF01194493 Verlag, Volltext: https://link.springer.com/article/10.1007/BF01194493 Verlag, Volltext: https://link.springer.com/content/pdf/10.1007%2FBF01194493.pdf 
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| Verfasserangaben: | E. Mammen, J.S. Marron, N.I. Fisher |
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| 520 | |a SummaryA 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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