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

Rousseau, Judith; Kruijer, Willem (2013), Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors, Electronic Journal of Statistics, 7, p. 2947-2969. http://dx.doi.org/10.1214/13-EJS864

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00672772
Date
2013
Journal name
Electronic Journal of Statistics
Volume
7
Publisher
The Institute of Mathematical Statistics and the Bernoulli Society
Pages
2947-2969
Publication identifier
http://dx.doi.org/10.1214/13-EJS864
Metadata
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Author(s)
Rousseau, Judith
Kruijer, Willem
Abstract (EN)
For a Gaussian time series with long-memory behavior, we use the FEXP-model for semi-parametric estimation of the long-memory parameter $d$. The true spectral density $f_o$ is assumed to have long-memory parameter $d_o$ and a FEXP-expansion of Sobolev-regularity $\be > 1$. We prove that when $k$ follows a Poisson or geometric prior, or a sieve prior increasing at rate $n^{\frac{1}{1+2\be}}$, $d$ converges to $d_o$ at a suboptimal rate. When the sieve prior increases at rate $n^{\frac{1}{2\be}}$ however, the minimax rate is almost obtained. Our results can be seen as a Bayesian equivalent of the result which Moulines and Soulier obtained for some frequentist estimators.
Subjects / Keywords
FEXP-priors; long memory models; bernstein von Mises; posterior concentration; Bayesian semi-parametric
JEL
C11 - Bayesian Analysis: General

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