Non-parametric density estimation methods are more flexible than parametric methods, due to the fact that they do not assume any specific shape or structure for the data. Most non-parametric methods, like Kernel estimation, require tuning of parameters to achieve good data smoothing, a non-trivial task, even in low dimensions. In higher dimensions, sparsity of data in local neighborhoods becomes a challenge even for non-parametric methods. In this paper, we use the copula transform and two efficient non-parametric methods to develop a new method for improved non-parametric density estimation in multivariate domain. After separation of marginal and joint densities using copula transform, a diffusion-based kernel estimator is employed to estimate the marginals. Next, Bayesian sequential partitioning (BSP) is used in the joint density estimation.

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使用 Copula 变换、贝叶斯序列划分和基于扩散的核估计器的非参数密度估计

非参数密度估计方法比参数方法更灵活，因为它们不假设数据的任何特定形状或结构。大多数非参数方法，如核估计，需要调整参数以实现良好的数据平滑，即使在低维中也是一项重要的任务。在更高维度上，即使对于非参数方法，局部邻域中数据的稀疏性也成为一个挑战。在本文中，我们使用 copula 变换和两种有效的非参数方法来开发一种新的方法来改进多元域中的非参数密度估计。在使用 copula 变换分离边缘和联合密度之后，采用基于扩散的核估计器来估计边缘。接下来，在联合密度估计中使用贝叶斯顺序分区 (BSP)。