Nearest neighbour bandwidth choice for nonparametric regression on mixtures with varying concentrations

Abstract: Finite mixture models naturally arise in statistical analysis of biological and sociological data. If the subpopulation which a subject belongs to is not known exactly, the distribution of its variables is a mixture of the subpopulations’ distributions. In the classical finite mixture models (FMM) the concentrations of the components in the mixture (mixing probabilities) are the same for all observations. In a more flexible mixture with varying concentrations model (MVC), the concentrations are different for different observations.

Regression models are typically applied to describe dependency between different numerical variables of one subject. In the case of homogeneous sample there 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 discontinuity (jump points). For such scenario, the LLRE stands as a remedy, having a significantly smaller bias.

In case of the MVC, we consider a modification of NWE (mNWE) and LLRE (mLLRE) for estimation of the regression function of a given component. Under suitable assumptions, these estimators are asymptotically normal, which makes it possible to derive theoretically optimal bandwidths. However, such bandwidths depend on unknown parameters of the underlying distributions and therefore cannot be used in practice.

In this talk, we propose an empirical bandwidth 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 measured by the asymptotic mean squared error (aMSE) or the asymptotic mean integrated squared error (aMISE).

probabilitystatistics theorydata analysis, statistics and probability

Audience: researchers in the topic

( chat )

---

Asymptotic Methods in Statistics

Series comments: One can find video files and slides of talks at the seminar on Asymptotic Methods in Statistics here: www.youtube.com/@SeminarforAsymptoticMethods

A link to a slide is below the description of the video, namely shorturl.at/jUAhL and shorturl.at/6wjUA shorturl.at/rdpqs

Alas the links do not work in one click: you should emphasize them with a mouse and select, e.g., "Go to shorturl.at/rdpqs".

---