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Existence and consistency of maximum likelihood in upgraded mixture models

Author

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  • van der Vaart, A. W.
  • Wellner, Jon A.

Abstract

Suppose one observes a sample of size m from the mixture density [integral operator] p(xz) d[eta](z) and a sample of size n from the distribution [eta]. The kernel p(xz) is known. We show existence of the maximum likelihood estimator for [eta], characterize its support, and prove consistency as m, n --> [infinity].

Suggested Citation

  • van der Vaart, A. W. & Wellner, Jon A., 1992. "Existence and consistency of maximum likelihood in upgraded mixture models," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 133-146, October.
    • Handle: RePEc:eee:jmvana:v:43:y:1992:i:1:p:133-146
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    Cited by:

    1. Wong, George Y. C. & Yu, Qiqing, 1999. "Generalized MLE of a Joint Distribution Function with Multivariate Interval-Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 155-166, May.
    2. Pan, Chun & Cai, Bo & Wang, Lianming & Lin, Xiaoyan, 2014. "Bayesian semiparametric model for spatially correlated interval-censored survival data," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 198-208.
    3. Pantazis, Nikos & Kenward, Michael G. & Touloumi, Giota, 2013. "Performance of parametric survival models under non-random interval censoring: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 16-30.
    4. Zhao, Xingqiu & Duan, Ran & Zhao, Qiang & Sun, Jianguo, 2013. "A new class of generalized log rank tests for interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 123-131.

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