关于大数据下非参数平滑化在线更新方法的推断  

Inference of online updating approach to nonparametric smoothing of big data

作　　者：陈子玉 郭潇 Chen Ziyu;Guo Xiao(Department of Statistics and Finance,School of Management,University of Science and Technology of China,Hefei 230026,China;International Institute of Finance,School of Management,University of Science and Technology of China,Hefei 230601,China)

机构地区：[1]中国科学技术大学管理学院统计与金融系,安徽合肥230026 [2]中国科学技术大学管理学院,国际金融研究院,安徽合肥230601

出　　处：《中国科学技术大学学报》2021年第5期390-403,共14页JUSTC

基　　金：supported by the National Natural Science Foundation of China(12071452,72091212,11601500);USTC Research Funds of the Double First-Class Initiative(YD2040002013).

摘　　要：在线更新方法是一种有效的大数据分析方法.本文证明了核密度和核回归在线模型的渐近性质,并进行了相应的统计推断.提出了几种算法分别解决了核密度和回归中带宽选择的困难.在模拟中验证了在线核密度模型的渐近正态性,并将在线线性核回归模型应用于波动率指数(VIX)预测.实证结果表明,与经典的局部线性回归模型相比,该模型在预测连续到达的期权数据流方面性能相当,但是计算复杂度显著降低.The online updating method(ONLINE)is an efficient analysis approach applied to big data.We prove the asymptotic properties and conduct statistical inference of the ONLINE models in kernel density and kernel regression.Several algorithms are proposed to solve the problems of the bandwidth selection in kernel density and regression respectively.We verify the asymptotic normality of the ONLINE density model in simulation and apply the ONLINE linear kernel regression to the Volatility Index(VIX)prediction.The empirical results show that the ONLINE linear kernel regression model achieves a comparable performance in continuously arriving option data streams prediction with significantly lower complexity than the classical local linear regression model.

关 键 词：带宽 核估计 在线更新方法 统计推断 波动率指数预测 

分 类 号：O212.7[理学—概率论与数理统计]