文章基本信息

标题：Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors
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作者：Willem Kruijer ; Judith Rousseau
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：2947-2969
DOI：10.1214/13-EJS864
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.