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Shape constrained kernel density estimation

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  • Birke, Melanie

Abstract

In this paper, a method for estimating monotone, convex and log-concave densities is proposed. The estimation procedure consists of an unconstrained kernel estimator which is modi?ed in a second step with respect to the desired shape constraint by using monotone rearrangements. It is shown that the resulting estimate is a density itself and shares the asymptotic properties of the unconstrained estimate. A short simulation study shows the ?nite sample behavior.

Suggested Citation

  • Birke, Melanie, 2008. "Shape constrained kernel density estimation," Technical Reports 2008,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200808
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    References listed on IDEAS

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    1. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Improving Estimates Of Monotone Functions By Rearrangement," Boston University - Department of Economics - Working Papers Series WP2007-012, Boston University - Department of Economics.
    2. Neumeyer, Natalie, 2007. "A note on uniform consistency of monotone function estimators," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 693-703, April.
    3. Dette, Holger & Volgushev, Stanislav, 2007. "Non-crossing nonparametric estimates of quantile curves," Technical Reports 2007,18, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Dette, Holger & Birke, Melanie, 2005. "A note on estimating a monotone regression by combining kernel and density estimates," Technical Reports 2005,24, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    Full references (including those not matched with items on IDEAS)

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