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A Bernstein-type estimator for decreasing density with application to p-value adjustments

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  • Han, Bing
  • Dalal, Siddhartha R.

Abstract

The nonparametric maximum likelihood estimator (NPMLE) is a popular approach to estimating decreasing densities, i.e., f(s)≥f(t),s≤t. A less ideal feature of NPMLE is its step-function form. In this paper, we propose two nonparametric density estimators based on the Bernstein-type polynomials of the NPMLE. The proposed estimators have relatively simple forms and easy implementation. They have satisfactory smoothness as well as estimation efficiency. Numerical examples demonstrate the superior performance of the proposed estimators compared to existing methods. Decreasing densities have been applied in simultaneous inference to estimate the proportion of true null hypotheses and the local false discovery rate. We applied the proposed estimators to conduct simultaneous tests for a gene expression data set.

Suggested Citation

  • Han, Bing & Dalal, Siddhartha R., 2012. "A Bernstein-type estimator for decreasing density with application to p-value adjustments," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 427-437.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:427-437
    DOI: 10.1016/j.csda.2011.08.010
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    References listed on IDEAS

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    1. Kim‐Anh Do & Peter Müller & Feng Tang, 2005. "A Bayesian mixture model for differential gene expression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 627-644, June.
    2. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
    3. Mette Langaas & Bo Henry Lindqvist & Egil Ferkingstad, 2005. "Estimating the proportion of true null hypotheses, with application to DNA microarray data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 555-572, September.
    4. Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100, January.
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