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Least squares estimation of a k-monotone density function

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  • Chee, Chew-Seng
  • Wang, Yong

Abstract

The fact that a k-monotone density can be defined by means of a mixing distribution makes its estimation feasible within the framework of mixture models. It turns the problem naturally into estimating a mixing distribution, nonparametrically. This paper studies the least squares approach to solving this problem and presents two algorithms for computing the estimate. The resulting mixture density is hence just the least squares estimate of the k-monotone density. Through simulated and real data examples, the usefulness of the least squares density estimator is demonstrated.

Suggested Citation

  • Chee, Chew-Seng & Wang, Yong, 2014. "Least squares estimation of a k-monotone density function," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 209-216.
    • Handle: RePEc:eee:csdana:v:74:y:2014:i:c:p:209-216
    DOI: 10.1016/j.csda.2014.01.007
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    References listed on IDEAS

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    1. Pavlides, Marios G. & Wellner, Jon A., 2012. "Nonparametric estimation of multivariate scale mixtures of uniform densities," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 71-89.
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    4. repec:dau:papers:123456789/4650 is not listed on IDEAS
    5. Chee, Chew-Seng & Wang, Yong, 2013. "Minimum quadratic distance density estimation using nonparametric mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 1-16.
    6. Mary Meyer & Desale Habtzghi, 2011. "Nonparametric estimation of density and hazard rate functions with shape restrictions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 455-470.
    7. Fadoua Balabdaoui & Jon A. Wellner, 2010. "Estimation of a k‐monotone density: characterizations, consistency and minimax lower bounds," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 45-70, February.
    Full references (including those not matched with items on IDEAS)

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