An effective estimation of multivariate density functions using extended-beta kernels with Bayesian adaptive bandwidths

TL;DR

This paper introduces a novel multivariate density estimation method using extended-beta kernels with Bayesian adaptive bandwidths, offering improved flexibility and accuracy over traditional kernels through theoretical analysis and simulation studies.

Contribution

The paper develops a new multivariate kernel density estimator with Bayesian adaptive bandwidths based on extended-beta kernels, providing theoretical properties and practical advantages.

Findings

The proposed estimator adapts well to dataset support boundaries.

Simulation results show improved accuracy over Gaussian and gamma kernels.

Applications demonstrate the method's flexibility and universality.

Abstract

Multivariate kernel density estimations have received much spate of interest. In addition to conventional methods of (non-)classical associated-kernels for (un)bounded densities and bandwidth selections, the multiple extended-beta kernel (MEBK) estimators with Bayesian adaptive bandwidths are invested to gain a deeper and better insight into the estimation of multivariate density functions. Being unimodal, the univariate extended-beta smoother has an adaptable compact support which is suitable for each dataset, always limited. The support of the density MBEK estimator can be known or estimated by extreme values. Thus, asymptotical properties for the (non-)normalized estimators are established. Explicit and general choices of bandwidths using the flexible Bayesian adaptive method are provided. Behavioural analyses, specifically undertaken on the sensitive edges of the estimator support, are studied and compared to Gaussian and gamma kernel estimators. Finally, simulation studies and three applications on original and usual real-data sets of the proposed method yielded very interesting advantages with respect to its flexibility as well as its universality.