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:20261115T003349Z 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\n\nAbstract\nFinite mixture mo dels naturally arise in statistical analysis of biological and sociologica l data. If the subpopulation which a subject belongs to is not known exact ly\, the distribution of its variables is a mixture of the subpopulations ’ distributions. In the classical finite mixture models (FMM) the concen trations of the components in the mixture (mixing probabilities) are the s ame for all observations. In a more flexible mixture with varying concentr ations model (MVC)\, the concentrations are different for different observ ations.\n\nRegression models are typically applied to describe dependency between different numerical variables of one subject. In the case of homog eneous sample there exist many nonparametric estimators of the regression function\, such as the Nadaraya-Watson estimator (NWE) and local linear re gression estimator (LLRE). For homogeneous samples\, NWE demonstrates an i nappropriate bias in points where the regressor probability density functi on (PDF) has discontinuity (jump points). For such scenario\, the LLRE sta nds as a remedy\, having a significantly smaller bias.\n\nIn case of the M VC\, we consider a modification of NWE (mNWE) and LLRE (mLLRE) for estimat ion of the regression function of a given component. Under suitable assump tions\, these estimators are asymptotically normal\, which makes it possib le to derive theoretically optimal bandwidths. However\, such bandwidths d epend on unknown parameters of the underlying distributions and therefore cannot be used in practice.\n\nIn this talk\, we propose an empirical band width choice for the mNWE and mLLRE based on a modification of the nearest neighbour technique. A simulation study shows that this approach performs satisfactorily compared with the theoretically optimal bandwidth\, as mea sured by the asymptotic mean squared error (aMSE) or the asymptotic mean i ntegrated squared error (aMISE).\n LOCATION:https://researchseminars.org/talk/AMIS/18/ END:VEVENT END:VCALENDAR