Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors

W.T. Kruijer, J. Rousseau

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

In this paper we study the semi-parametric problem of the estimation of the long-memory parameter d in a Gaussian long-memory model. Considering a family of priors based on FEXP models, called FEXP priors in Rousseau et al. (2012), we derive concentration rates together with a Bernstein-von Mises theorem for the posterior distribution of d, under Sobolev regularity conditions on the short-memory part of the spectral density. Three different variations on the FEXP priors are studied. We prove that one of them leads to the minimax (up to a logn term) posterior concentration rate for d, under Sobolev conditions on the short memory part of the spectral density, while the other two lead to sub-optimal posterior concentration rates in d. Interestingly these results are contrary to those obtained in Rousseau et al. (2012) for the global estimation of the spectral density.
Original languageEnglish
Pages (from-to)2947-2969
JournalElectronic Journal of Statistics
Volume7
DOIs
Publication statusPublished - 2013

Keywords

  • von-mises theorem
  • posterior distributions
  • adaptive estimation
  • linear-regression
  • convergence-rates
  • spectral density
  • models

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