A hybrid nonparametric multivariate density estimator with applications to risk management
提出一种混合密度估计器，结合核估计与指数级数估计的优势，通过阈值选择基函数和蒙特卡洛积分计算归一化因子，数值模拟和金融风险管理应用显示其良好性能。
.Multivariate density estimation is plagued by the curse of dimensionality in theory and practice. We propose a hybrid density estimator of a multivariate density f that combines the strengths of the kernel estimator and the exponential series estimator. This estimator refines a preliminary kernel estimate f̂0 with a multiplicative correction that estimates the ratio r=f/f̂0 with an exponential series estimator. Thanks to the consistency of the pilot estimate, the coefficients of the series expansion tend to approach zero asymptotically. Accordingly, we design a thresholding method for basis function selection. A major obstacle of multivariate exponential series estimator is the calculation of its normalization factor. We resolve this difficulty with Monte Carlo integration, using the pilot kernel estimate as the trial density for importance sampling. This approach greatly enhances the practicality of the hybrid estimator. Numerical simulations demonstrate the good finite sample performance of the hybrid estimator. We present one empirical application in financial risk management.