Fully Data-Driven Normalized and Exponentiated Kernel Density Estimator with Hyvärinen Score
提出一种全数据驱动的指数化核密度估计器，通过Hyvärinen评分优化两个超参数，避免归一化常数计算，适用于多峰或含异常值的数据分布。
Recently, Jewson and Rossell proposed a new approach for kernel density estimation using an exponentiated form of kernel density estimators. The density estimator contained two hyperparameters that flexibly controls 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 caused by 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 promising when the underlying density is multi-modal or when observations contain outliers.