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2013 Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors
Willem Kruijer, Judith Rousseau
Electron. J. Statist. 7: 2947-2969 (2013). DOI: 10.1214/13-EJS864


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 $\log n$ 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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Willem Kruijer. Judith Rousseau. "Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors." Electron. J. Statist. 7 2947 - 2969, 2013.


Received: 1 April 2013; Published: 2013
First available in Project Euclid: 13 December 2013

zbMATH: 1349.62100
MathSciNet: MR3151758
Digital Object Identifier: 10.1214/13-EJS864

Primary: 62G20
Secondary: 62M15

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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