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Smooth density estimation with moment constraints using mixture distributions

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  • Ani Eloyan
  • Sujit Ghosh

Abstract

Statistical analysis often involves the estimation of a probability density based on a sample of observations. A commonly used nonparametric method for solving this problem is the kernel-based method. The motivation is that any continuous density can be approximated by a mixture of densities with appropriately chosen bandwidths. In many practical applications, we may have specific information about the moments of the density. A nonparametric method using a mixture of known densities is proposed that conserves a given set of moments. A modified expectation–maximisation algorithm for estimating the weights of the mixture density is then developed. The proposed method also obtains an estimate of the number of components in the mixture needed for optimal approximation. The proposed method is compared with two popular density estimation methods using simulated data and it is shown that the proposed estimate outperforms the others. The method is then illustrated by applying it to several real-data examples.

Suggested Citation

  • Ani Eloyan & Sujit Ghosh, 2011. "Smooth density estimation with moment constraints using mixture distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 513-531.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:513-531
    DOI: 10.1080/10485252.2010.532554
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    References listed on IDEAS

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    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. Wendimagegn Ghidey & Emmanuel Lesaffre & Paul Eilers, 2004. "Smooth Random Effects Distribution in a Linear Mixed Model," Biometrics, The International Biometric Society, vol. 60(4), pages 945-953, December.
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    Cited by:

    1. Bao, Junshu & Hanson, Timothy E., 2016. "A mean-constrained finite mixture of normals model," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 93-99.
    2. Kun Meng & Ani Eloyan, 2021. "Principal manifold estimation via model complexity selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 369-394, April.
    3. Eloyan, Ani & Ghosh, Sujit K., 2013. "A semiparametric approach to source separation using independent component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 383-396.
    4. Kuangyu Wen & Ximing Wu & David J. Leatham, 2021. "Spatially Smoothed Kernel Densities with Application to Crop Yield Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 349-366, September.

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