Study of Data-driven Uncertain Set Based on Robust Kernel Density Estimation

• 1、College of Mathematics and Statistics, Chongqing University,Chongqing 401331
• 2、College of Mathematics and Statistics, Chongqing Jiaotong University,Chongqing 400074

Abstract：In this paper, robustkernel density estimation in non-parametric estimation is used to estimate the true density function effectively. Under L1 distance, the uncertainty set is constructed by the distribution function corresponding to the robustkernel density estimation function and the true density function respectively, so that the uncertainty set fully contains the informations of the distribution function corresponding to the random variable.Firstly, the gaussian kernel density estimation function and the robust gaussian kernel density estimation function are introduced and the consistency of the two estimation functions is proved.Then the iterative reweighted least square method is used to select the weights of the robust gaussian kernel density estimation function, and the k-nearest neighbor method is used to calculate the smoothing parameters corresponding to each observed value.Then the performance of the robust kernel density estimation method is analyzed.Finally, the definition of a data-driven uncertainty set based on historical observations and L1 distance is given, and the two-stage robust optimization model under the uncertainty set is transformed into a corresponding linear model which can be easily handled.

Keywords： Operations research and cybernetics Robust kernel density estimation Two-stage robust optimization Data-driven uncertaintyset Gaussian kernel