Nonparametric density estimation from observations with multiplicative measurement errors

Denis Belomestny, Alexander Goldenshluger

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In particular, we show that, depending on whether this point is separated away from zero or not, there are two different regimes in terms of the rates of convergence of the minimax risk. In both regimes we develop kernel-type density estimators and prove upper bounds on their maximal risk over suitable nonparametric classes of densities. We show that the proposed estimators are rate-optimal by establishing matching lower bounds on the minimax risk. Finally we test our estimation procedures on simulated data.

Original languageEnglish
Pages (from-to)36-37
Number of pages2
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume56
Issue number1
DOIs
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 Association des Publications de l'Institut Henri Poincaré.

Keywords

  • Density estimation
  • Multiplicative censoring
  • Multiplicative measurement errors
  • Scale mixtures
  • The Mellin transform

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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