{"paper":{"title":"Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"CREST), Judith Rousseau (CEREMADE, Willem Kruijer","submitted_at":"2012-02-22T09:09:13Z","abstract_excerpt":"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 th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4863","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}