State Key Laboratory of Microbial Metabolism, School of Life Sciences and Biotechnology, Shanghai Jiao Tong University, Shanghai, China.
Institute of Biochemistry and Cell Biology, Chinese Academy of Sciences, Shanghai, China.
Interdiscip Sci. 2019 Sep;11(3):559-574. doi: 10.1007/s12539-019-00343-w. Epub 2019 Jul 17.
Nonparametric estimation of cumulative distribution function and probability density function of continuous random variables is a basic and central problem in probability theory and statistics. Although many methods such as kernel density estimation have been presented, it is still quite a challenging problem to be addressed to researchers. In this paper, we proposed a new method of spline regression, in which the spline function could consist of totally different types of functions for each segment with the result of Monte Carlo simulation. Based on the new spline regression, a new method to estimate the distribution and density function was provided, which showed significant advantages over the existing methods in the numerical experiments. Finally, the density function estimation of high dimensional random variables was discussed. It has shown the potential to apply the method in classification and regression models.
连续型随机变量的累积分布函数和概率密度函数的非参数估计是概率论和统计学中的一个基本和核心问题。尽管已经提出了许多方法，如核密度估计，但对于研究人员来说，这仍然是一个具有挑战性的问题。在本文中，我们提出了一种新的样条回归方法，其中样条函数可以在每个分段中由完全不同类型的函数组成，结果是蒙特卡罗模拟。基于新的样条回归，提供了一种新的方法来估计分布和密度函数，在数值实验中，该方法明显优于现有的方法。最后，讨论了高维随机变量的密度函数估计。结果表明，该方法在分类和回归模型中有应用的潜力。
