论文标题
完全数据驱动的归一化和凸起的内核密度估计器，hyvärinen评分
Fully Data-driven Normalized and Exponentiated Kernel Density Estimator with Hyvärinen Score
论文作者
论文摘要
我们使用内核密度估计器的凸起形式引入了新的内核密度估计。密度估计器具有两个高参数，可以灵活地控制所得密度的平滑度。我们通过基于Hyvärinen评分最小化目标函数，以数据驱动的方式调整它们，以避免优化，涉及由于凸起而导致的棘手归一化常数。我们显示了所提出的估计量的渐近特性，并强调将两个超参数用于柔性密度估计的重要性。我们的模拟研究和对收入数据的应用表明，当潜在的密度为多模式或观察值时，提出的密度估计器在吸引人。
We introduce a new deal of kernel density estimation using an exponentiated form of kernel density estimators. The density estimator has two hyperparameters flexibly controlling the smoothness of the resulting density. We tune them in a data-driven manner by minimizing an objective function based on the Hyvärinen score to avoid the optimization involving the intractable normalizing constant due to the exponentiation. We show the asymptotic properties of the proposed estimator and emphasize the importance of including the two hyperparameters for flexible density estimation. Our simulation studies and application to income data show that the proposed density estimator is appealing when the underlying density is multi-modal or observations contain outliers.
