Estimating the mean of high valued observations in high dimensions

Eitan Greenshtein, Junyong Park, Ya’Acov Ritov

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Let Yi ~ N(μi,1), i = 1,…, n, be independent random variables. We study the problem of estimating the quantity S = Σ{i|C<Yii. We emphasize the case where n is large, the vector (μ1,…,μn) is sparse, and the value of C is large. Our approach is nonparametric empirical Bayes, where μi are assumed i.i.d from an unknown G. The performance of our suggested estimator is studied both theoretically and through simulations. We also obtain some results related to the local false discovery rates corresponding to high valued points Yi.

Original languageEnglish
Pages (from-to)408-418
Number of pages11
JournalJournal of Statistical Theory and Practice
Volume2
Issue number3
DOIs
StatePublished - 2008

Keywords

  • Empirical Bayes
  • FDR
  • Sparse vector

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