Multivariate Density Estimation with Missing Data

TL;DR

This paper introduces a flexible mixture model for multivariate density estimation with missing data, enabling effective imputation and demonstrating superior performance through simulations and case studies.

Contribution

It proposes a novel mixture of tensor product kernels approach that simplifies imputation with Gibbs sampling for multivariate data with missing entries.

Findings

Outperforms existing imputation methods in simulations

Effective in handling heteroskedasticity in regression models

Demonstrated success in real case studies

Abstract

Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when observations are missing in one or more variables of the multivariate vector. A flexible class of mixture of tensor products of kernel densities is proposed which allows for easy implementation of imputation methods using Gibbs sampling and shown to have superior performance compared to some of the exisiting imputation methods currently available in literature. Numerical illustrations are provided using several simulated data scenarios and applications to couple of case studies are also presented.