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.

翻译：本文提出了一种直观的多元核密度估计（KDE）方法用于数据校正。该方法利用条件概率密度函数（PDF）的期望值及可信区间来量化校正的不确定性。我们提出了一种选择性KDE因子，用于调整核函数的尺寸和形状，该因子通过最小二乘交叉验证（LSCV）或均方条件误差（MCSE）准则确定。选择性带宽方法可与自适应方法结合使用，以潜在提高精度。通过一个假设数据集和一个实际数据集的实例验证了该方法的有效性。选择性带宽方法始终优于非选择性方法，而自适应带宽方法改善了假设数据集的结果，但对实际数据集效果不佳。MCSE准则能够最小化均方根误差，但可能导致分布欠平滑，而LSCV准则则在PDF拟合度与低均方根误差之间取得了平衡。