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Estimation of Dirichlet process priors with monotone missing data

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  • Lei Yang
  • Xianyi Wu

Abstract

This article investigates the estimation of Dirichlet process priors DP(α, α¯) of a random ( J +1)-dimensional distribution by monotone missing observations, where the precision parameter α is a positive scalar and α¯ a probability measure on ℝ-super- J +1. While α is estimated by maximising a particularly designed likelihood function, α¯ is estimated using kernel smoothing. The asymptotic properties show that the estimate of α is strongly consistent and asymptotically normally distributed. For the estimate of α¯, the L 1 consistency and the optimal bandwidths under an asymptotic mean integrated squared error criterion are examined. Finally, the performance of these estimates are analysed by means of a small simulation.

Suggested Citation

  • Lei Yang & Xianyi Wu, 2013. "Estimation of Dirichlet process priors with monotone missing data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 787-807, December.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:787-807
    DOI: 10.1080/10485252.2013.804074
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    References listed on IDEAS

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    1. Paul D. Allison, 2000. "Multiple Imputation for Missing Data," Sociological Methods & Research, , vol. 28(3), pages 301-309, February.
    2. Devroye, Luc & Krzyzak, Adam, 2002. "New Multivariate Product Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 88-110, July.
    3. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
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    Cited by:

    1. Jianjun Zhang & Lei Yang & Xianyi Wu, 2019. "Polya tree priors and their estimation with multi-group data," Statistical Papers, Springer, vol. 60(3), pages 849-875, June.

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