Electronic Journal of Statistics

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

Willem Kruijer and Judith Rousseau

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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.

Article information

Electron. J. Statist., Volume 7 (2013), 2947-2969.

Received: April 2013
First available in Project Euclid: 13 December 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G20: Asymptotic properties
Secondary: 62M15: Spectral analysis

Bayesian semi-parametric Bernstein-von Mises FEXP priors Gaussian long-memory processes rates of convergence


Kruijer, Willem; Rousseau, Judith. Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors. Electron. J. Statist. 7 (2013), 2947--2969. doi:10.1214/13-EJS864. https://projecteuclid.org/euclid.ejs/1386943909

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