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For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of the homogenized dynamics. Our first estimator is derived from a martingale estimating function of the generator of the homogenized diffusion process. However, the unbiasedness of the estimator depends on the rate with which the observations are sampled. We therefore introduce a second estimator which relies also on filtering the data, and we prove that it is asymptotically unbiased independently of the sampling rate. A series of numerical experiments illustrate the reliability and efficiency of our different estimators.<\/jats:p>","DOI":"10.1007\/s11222-022-10081-7","type":"journal-article","created":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T12:04:09Z","timestamp":1649678649000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5687-9742","authenticated-orcid":false,"given":"Assyr","family":"Abdulle","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Grigorios A.","family":"Pavliotis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Zanoni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,11]]},"reference":[{"key":"10081_CR1","doi-asserted-by":"publisher","first-page":"1565","DOI":"10.1137\/20M1348431","volume":"18","author":"A Abdulle","year":"2020","unstructured":"Abdulle, A., Garegnani, G., Zanoni, A.: Ensemble Kalman filter for multiscale inverse problems. 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