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- W4299425582 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 $log n$ 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." @default.
- W4299425582 created "2022-10-02" @default.
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- W4299425582 date "2013-01-01" @default.
- W4299425582 modified "2023-09-30" @default.
- W4299425582 title "Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors" @default.
- W4299425582 doi "https://doi.org/10.1214/13-ejs864" @default.
- W4299425582 hasPublicationYear "2013" @default.
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