Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors
type: Dataset
description: 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.
issued: 2026-05-27T15:12:59.448139
language: en
modified: 2026-05-27T15:12:59.448145
contact point: Organization
  fn: CCSD
keyword: bayesian-semi-parametric
keyword: bernstein-von-mises
keyword: infoeu-reposemanticspreprint
keyword: long-memory-models
keyword: mathmath-stmathematics-mathstatistics-mathst
keyword: posterior-concentration
keyword: preprints-working-papers-
keyword: statthstatistics-statstatistics-theory-statth
landing page: https://hal.science/hal-00672772

Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors
type: Distribution
format: HTML
issued: 2026-05-27T15:12:59.475806
modified: 2026-05-27T15:12:59.424988
access URL: https://hal.science/hal-00672772

test_moissonnage_selune
type: Agent