{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:40:27Z","timestamp":1760132427122,"version":"3.37.3"},"reference-count":24,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-15-CE05-0024"],"award-info":[{"award-number":["ANR-15-CE05-0024"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We design and analyze an algorithm for estimating the mean of a\nfunction of a conditional expectation when the outer expectation is related\nto a rare event. The outer expectation is evaluated through the average along\nthe path of an ergodic Markov chain generated by a Markov chain Monte Carlo\nsampler. The inner conditional expectation is computed as a non-parametric\nregression, using a least-squares method with a general function\nbasis and a design given by the sampled Markov chain. We\nestablish non-asymptotic bounds for the <jats:inline-formula id=\"j_mcma-2017-0101_ineq_9999_w2aab2b8d876b1b7b1aab1c13b1b1Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>L<\/m:mi>\n                              <m:mn>2<\/m:mn>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" content-type=\"j_mcma-2017-0101_ineq_9999\" xlink:href=\"graphic\/j_mcma-2017-0101_eq_mi224.png\"\/>\n                        <jats:tex-math>${L_{2}}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-empirical risks associated to\nthis least-squares regression; this generalizes the error bounds usually\nobtained in the case of i.i.d. observations. Global error bounds are also\nderived for the nested expectation problem. Numerical results in the context\nof financial risk computations illustrate the performance of the algorithms.<\/jats:p>","DOI":"10.1515\/mcma-2017-0101","type":"journal-article","created":{"date-parts":[[2017,2,3]],"date-time":"2017-02-03T09:44:43Z","timestamp":1486115083000},"page":"21-42","source":"Crossref","is-referenced-by-count":7,"title":["MCMC design-based non-parametric regression for rare event. Application to nested risk computations"],"prefix":"10.1515","volume":"23","author":[{"given":"Gersende","family":"Fort","sequence":"first","affiliation":[{"name":"LTCI, CNRS, T\u00e9l\u00e9com ParisTech, Universit\u00e9 Paris-Saclay, 75013, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emmanuel","family":"Gobet","sequence":"additional","affiliation":[{"name":"Centre de Math\u00e9matiques Appliqu\u00e9es (CMAP), Ecole Polytechnique and CNRS, Universit\u00e9 Paris-Saclay, Route de Saclay, 91128 Palaiseau Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric","family":"Moulines","sequence":"additional","affiliation":[{"name":"Centre de Math\u00e9matiques Appliqu\u00e9es (CMAP), Ecole Polytechnique and CNRS, Universit\u00e9 Paris-Saclay,Route de Saclay, 91128 Palaiseau Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,2,3]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Baraud Y., Comte F. and Viennet G.,\nAdaptive estimation in autoregression or \u03b2-mixing regression via model selection,\nAnn. 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