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DTSTART;TZID=Europe/Helsinki:20260518T140000
DTEND;TZID=Europe/Helsinki:20260518T153000
DTSTAMP:20260709T184502
CREATED:20260505T072839Z
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UID:18945-1779112800-1779118200@crest.science
SUMMARY:Yannick BARAUD (Université du Luxembourg) - A Robust Alternative to Least Squares in Regression
DESCRIPTION:Statistical Seminar: Every Monday at 2:00 pm.\nTime: 2:00 pm – 3:00 pm\nDate: 18th May\nPlace: 3001 \nYannick BARAUD (Université du Luxembourg) – A Robust Alternative to Least Squares in Regression \n Abstract:  \nIn collaboration with Guillaume Maillard\, we study the estimation of a regression function under weak assumptions on the error distribution. In particular\, we do not assume that the errors are i.i.d.\, nor that they have finite variance or exponential moments; we only require them to be independent and centered (and hence integrable). In particular\, when the errors are square-integrable\, they may\, for instance\, be heteroscedastic. \nWithin this statistical framework\, we introduce a generic estimation method that yields estimators whose performance automatically adapts to the integrability properties of the errors. For these estimators\, we establish non-asymptotic risk bounds for the L_1-loss. When the regression function belongs to a linear space and the errors are Gaussian but not necessarily i.i.d.\, these estimators exhibit remarkable robustness properties: they may converge at parametric rate (up to a logarithmic factor) in situations where classical least squares is not even consistent. \nNevertheless\, we mainly illustrate their properties in the context of estimating a regression function under a shape constraint\, such as monotonicity\, unimodality\, or convexity. We show that the proposed estimator is not only robust with respect to this a priori shape assumption\, but also exhibits adaptation properties which are similar to those established for the least squares under the additional assumptions that the errors are i.i.d. and square-integrable. \nOrganizers: \nAnna KORBA (CREST)\, Vincent DIVOL (CREST) \, Jaouad MOURTADA (CREST) \nSponsors:\nCREST-CMAP \n
URL:https://crest.science/event/yannick-baraud-universite-du-luxembourg-a-robust-alternative-to-least-squares-in-regression/
CATEGORIES:Seminars,Statistics
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