Inference for a two-component mixture of symmetric distributions under log-concavity

Fadoua Balabdaoui, Charles R. Doss

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

In this article, we revisit the problem of estimating the unknown zero-symmetric distribution in a twocomponent location mixture model, considered in previous works, now under the assumption that the zerosymmetric distribution has a log-concave density. When consistent estimators for the shift locations and mixing probability are used, we show that the nonparametric log-concave Maximum Likelihood estimator (MLE) of both the mixed density and that of the unknown zero-symmetric component are consistent in the Hellinger distance. In case the estimators for the shift locations and mixing probability are √n-consistent, we establish that these MLE's converge to the truth at the rate n-2/5 in the L1 distance. To estimate the shift locations and mixing probability, we use the estimators proposed by (Ann. Statist. 35 (2007) 224-251). The unknown zero-symmetric density is efficiently computed using the R package logcondens.mode.

Original languageEnglish (US)
Pages (from-to)1053-1071
Number of pages19
JournalBernoulli
Volume24
Issue number2
DOIs
StatePublished - May 2018

Keywords

  • Bracketing entropy
  • Consistency
  • Empirical processes
  • Global rate
  • Hellinger metric
  • Log-concave
  • Mixture
  • Symmetric

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