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    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

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Record number 445740
Title Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors
Author(s) Kruijer, W.T.; Rousseau, J.
Source Electronic Journal of Statistics 7 (2013). - ISSN 1935-7524 - p. 2947 - 2969.
Department(s) Mathematical and Statistical Methods - Biometris
Publication type Refereed Article in a scientific journal
Publication year 2013
Keyword(s) von-mises theorem - posterior distributions - adaptive estimation - linear-regression - convergence-rates - spectral density - models
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.
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