BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:PhD student Daniel Gorbunov (Taras Shevchenko National University of Kyiv) DTSTART:20260513T140000Z DTEND:20260513T150000Z DTSTAMP:20260512T105021Z UID:AMIS/6 DESCRIPTION:Title: Non parametric regression estimators for mixtures with varying concentrations< /a>\nby PhD student Daniel Gorbunov (Taras Shevchenko National University of Kyiv) as part of Asymptotic Methods in Statistics\n\nInteractive livest ream: https://knu-ua.zoom.us/j/89643295643?pwd=eTBZZSt0d0thZzFyaUhDUFNGTVE 3QT09 Passcode (if necessary) 785163\n\nAbstract\nFinite mixture models n aturally arise in statistical analysis of biological and sociological data . If the sub-population which a subject belongs to is not known exactly\, the distribution of its variables is a mixture of the sub-populations’ d istributions. In the classical finite mixture models (FMM) the concentrati ons of the components in the mixture (mixing probabilities) are the same f or all observations. In a more flexible mixture with varying concentration s model (MVC)\, the concentrations are different for different observation s.\n\nRegression models are typically applied to describe dependency betwe en different numerical variables of one subject. In the case of homogeneou s sample there exist many non-parametric estimators of the regression func tion\, such as the Nadaraya-Watson estimator (NWE) and local linear regres sion estimator (LLRE). For homogeneous samples\, NWE demonstrates an inapp ropriate bias in points where the regressor probability density function ( PDF) has discontinuity (jump points). For such a scenario\, the LLRE stand s as a remedy\, having a significantly smaller bias.\n\nIn this talk\, we consider a modification of NWE (mNWE) and LLRE (mLLRE) for the estimation of the regression function of some MVC component. We will show that under suitable assumptions\, the modified estimators are asymptotically normal. Moreover\, the rate of convergence for the mNWE is different at different points of continuity and discontinuity of the regressor's PDF respectively \, whereas the mLLRE preserves the same rate of convergence for both cases .\n LOCATION:https://researchseminars.org/talk/AMIS/6/ URL:https://knu-ua.zoom.us/j/89643295643?pwd=eTBZZSt0d0thZzFyaUhDUFNGTVE3Q T09 Passcode (if necessary) 785163 END:VEVENT END:VCALENDAR