NONPARAMETRIC DENSITY ESTIMATION BY B-SPLINE DUALITY
提出一种基于框架和Riesz基理论的新非参数密度估计方法，利用B样条构造双正交密度估计量，推导渐近最优带宽选择，适用于金融和经济市场的高频数据分析。
In this article, we propose a new nonparametric density estimator derived from the theory of frames and Riesz bases. In particular, we propose the so-called bi-orthogonal density estimator based on the class of B-splines and derive its theoretical properties, including the asymptotically optimal choice of bandwidth. Detailed theoretical analysis and comparisons of our estimator with existing local basis and kernel density estimators are presented. The estimator is particularly well suited for high-frequency data analysis in financial and economic markets.