Application of Multivariate Selective Bandwidth Kernel Density Estimation for Data Correction

TL;DR

This paper introduces a multivariate kernel density estimation approach with selective bandwidth adjustment for data correction, demonstrating improved accuracy over traditional methods through examples.

Contribution

It proposes a novel selective bandwidth method for KDE that enhances data correction accuracy by optimizing kernel size and shape using LSCV or MCSE criteria.

Findings

Selective bandwidth methods outperform non-selective methods.

Adaptive bandwidth improves results for hypothetical data but not for real data.

LSCV balances PDF fit and RMSE, while MCSE minimizes RMSE but may under-smooth.

Abstract

This paper presents an intuitive application of multivariate kernel density estimation (KDE) for data correction. The method utilizes the expected value of the conditional probability density function (PDF) and a credible interval to quantify correction uncertainty. A selective KDE factor is proposed to adjust both kernel size and shape, determined through least-squares cross-validation (LSCV) or mean conditional squared error (MCSE) criteria. The selective bandwidth method can be used in combination with the adaptive method to potentially improve accuracy. Two examples, involving a hypothetical dataset and a realistic dataset, demonstrate the efficacy of the method. The selective bandwidth methods consistently outperform non-selective methods, while the adaptive bandwidth methods improve results for the hypothetical dataset but not for the realistic dataset. The MCSE criterion minimizes root mean square error but may yield under-smoothed distributions, whereas the LSCV criterion strikes a balance between PDF fitness and low RMSE.