Application of Multivariate Selective Bandwidth Kernel Density Estimation for Data Correction

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.