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:20260602T062621Z 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\n\nAbstract\nFinite mixture models naturally 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’ distributions. In the classical finite mixture models (FMM ) the concentrations of the components in the mixture (mixing probabilitie s) are the same for all observations. In a more flexible mixture with vary ing concentrations model (MVC)\, the concentrations are different for diff erent observations.\n\nRegression models are typically applied to describe dependency between different numerical variables of one subject. In the c ase of homogeneous sample there exist many non-parametric estimators of th e regression function\, such as the Nadaraya-Watson estimator (NWE) and lo cal linear regression estimator (LLRE). For homogeneous samples\, NWE demo nstrates an inappropriate bias in points where the regressor probability d ensity function (PDF) has discontinuity (jump points). For such a scenario \, the LLRE stands as a remedy\, having a significantly smaller bias.\n\nI n this talk\, we consider a modification of NWE (mNWE) and LLRE (mLLRE) fo r the estimation of the regression function of some MVC component. We will show that under suitable assumptions\, the modified estimators are asympt otically normal. Moreover\, the rate of convergence for the mNWE is differ ent at different points of continuity and discontinuity of the regressor's PDF respectively\, whereas the mLLRE preserves the same rate of convergen ce for both cases.\n LOCATION:https://researchseminars.org/talk/AMIS/6/ END:VEVENT END:VCALENDAR