BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:PhD student Daniel Horbunov (Taras Shevchenko National University of Kyiv and EPFL\, Lausanne\, Switzerland) DTSTART:20261028T150000Z DTEND:20261028T160000Z DTSTAMP:20261025T111744Z UID:AMIS/18 DESCRIPTION:Title: Ne arest neighbour bandwidth choice for nonparametric regression on mixtures with varying concentrations\nby PhD student Daniel Horbunov (Taras Sh evchenko National University of Kyiv and EPFL\, Lausanne\, Switzerland) as part of Asymptotic Methods in Statistics\n\nInteractive livestream: https ://knu-ua.zoom.us/j/89643295643?pwd=eTBZZSt0d0thZzFyaUhDUFNGTVE3QT09 Pass code (if necessary) 785163\n\nAbstract\nFinite mixture models naturally ar ise in statistical analysis of biological and sociological data. If the su bpopulation which a subject belongs to is not known exactly\, the distribu tion of its variables is a mixture of the subpopulations’ distributions. In the classical finite mixture models (FMM) the concentrations of the co mponents in the mixture (mixing probabilities) are the same for all observ ations. In a more flexible mixture with varying concentrations model (MVC) \, the concentrations are different for different observations.\n\nRegress ion models are typically applied to describe dependency between different numerical variables of one subject. In the case of homogeneous sample ther e exist many nonparametric estimators of the regression function\, such as the Nadaraya-Watson estimator (NWE) and local linear regression estimator (LLRE). For homogeneous samples\, NWE demonstrates an inappropriate bias in points where the regressor probability density function (PDF) has disco ntinuity (jump points). For such scenario\, the LLRE stands as a remedy\, having a significantly smaller bias.\n\nIn case of the MVC\, we consider a modification of NWE (mNWE) and LLRE (mLLRE) for estimation of the regress ion function of a given component. Under suitable assumptions\, these esti mators are asymptotically normal\, which makes it possible to derive theor etically optimal bandwidths. However\, such bandwidths depend on unknown p arameters of the underlying distributions and therefore cannot be used in practice.\n\nIn this talk\, we propose an empirical bandwidth choice for t he mNWE and mLLRE based on a modification of the nearest neighbour techniq ue. A simulation study shows that this approach performs satisfactorily co mpared with the theoretically optimal bandwidth\, as measured by the asymp totic mean squared error (aMSE) or the asymptotic mean integrated squared error (aMISE).\n LOCATION:https://researchseminars.org/talk/AMIS/18/ URL:https://knu-ua.zoom.us/j/89643295643?pwd=eTBZZSt0d0thZzFyaUhDUFNGTVE3Q T09 Passcode (if necessary) 785163 END:VEVENT END:VCALENDAR