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Simultaneous estimation based on empirical likelihood and general maximum likelihood estimation

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  • Park, Junyong

Abstract

One typical problem in simultaneous estimation of mean values is estimating means of normal distributions, however when normality or any other distribution is not specified, more robust estimation procedures are demanded. A new estimation procedure is proposed based on empirical likelihood which does not request any specific distributional assumption. The new idea is based on incorporating empirical likelihood with general maximum likelihood estimation. One well-known nonparametric estimator, the linear empirical Bayes estimator, can be interpreted as an estimator based on empirical likelihood under some framework and it is shown that the proposed procedure can improve the linear empirical Bayes estimator. Numerical studies are presented to compare the proposed estimator with some existing estimators. The proposed estimator is applied to the problem of estimating mean values corresponding to high valued observations. Simulations and real data example of gene expression are provided.

Suggested Citation

  • Park, Junyong, 2018. "Simultaneous estimation based on empirical likelihood and general maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 19-31.
    • Handle: RePEc:eee:csdana:v:117:y:2018:i:c:p:19-31
    DOI: 10.1016/j.csda.2017.08.003
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    References listed on IDEAS

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    1. Junyong Park, 2012. "Nonparametric empirical Bayes estimator in simultaneous estimation of Poisson means with application to mass spectrometry data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 245-265.
    2. Erickson Stephen & Sabatti Chiara, 2005. "Empirical Bayes Estimation of a Sparse Vector of Gene Expression Changes," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-27, September.
    3. Roger Koenker & Ivan Mizera, 2014. "Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 674-685, June.
    4. Xianchao Xie & S. C. Kou & Lawrence D. Brown, 2012. "SURE Estimates for a Heteroscedastic Hierarchical Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1465-1479, December.
    5. Lawrence D. Brown & Eitan Greenshtein & Ya'acov Ritov, 2013. "The Poisson Compound Decision Problem Revisited," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 741-749, June.
    6. Koenker, Roger & Mizera, Ivan, 2014. "Convex Optimization in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i05).
    7. Efron, Bradley, 2009. "Empirical Bayes Estimates for Large-Scale Prediction Problems," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1015-1028.
    8. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
    9. Park, Junyong, 2014. "Shrinkage estimator in normal mean vector estimation based on conditional maximum likelihood estimators," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 1-6.
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