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\({\mathcal{M}}\) -decomposability and symmetric unimodal densities in one dimension

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Abstract

In this paper, we introduce the notion of \({\mathcal{M}}\) -decomposability of probability density functions in one dimension. Using \({\mathcal{M}}\) -decomposability, we derive an inequality that applies to all symmetric unimodal densities. Our inequality involves only the standard deviation of the densities concerned. The concept of \({\mathcal{M}}\) -decomposability can be used as a non-parametric criterion for mode-finding and cluster analysis.

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Authors and Affiliations

  1. Department of Statistical Science, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies, Tokyo, Japan

    Nicholas Chia

  2. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, 106-8569, Japan

    Nicholas Chia & Junji Nakano

Authors
  1. Nicholas Chia
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  2. Junji Nakano
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Correspondence to Nicholas Chia.

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Chia, N., Nakano, J. \({\mathcal{M}}\) -decomposability and symmetric unimodal densities in one dimension. Ann Inst Stat Math 61, 275–289 (2009). https://doi.org/10.1007/s10463-007-0144-2

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  • DOI: https://doi.org/10.1007/s10463-007-0144-2

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