关于大数据下非参数平滑化在线更新方法的推断

doi:10.52396/JUST-2021-0078

中国科学技术大学学报 ›› 2021, Vol. 51 ›› Issue (5): 390-403.DOI: 10.52396/JUST-2021-0078

关于大数据下非参数平滑化在线更新方法的推断

陈子玉¹, 郭潇^2*

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

收稿日期:2021-03-17 修回日期:2021-05-20 出版日期:2021-05-31 发布日期:2021-12-01
通讯作者: * E-mail:xiaoguo@ustc.edu.cn

Inference of online updating approach to nonparametric smoothing of big data

Chen Ziyu¹, Guo Xiao^2*

1.Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China;
2.International Institute of Finance, School of Management, University of Science and Technology of China, Hefei 230601, China

Received:2021-03-17 Revised:2021-05-20 Online:2021-05-31 Published:2021-12-01
Contact: * E-mail: xiaoguo@ustc.edu.cn

摘要/Abstract

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.

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

Abstract: 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.

Key words: bandwidth, kernel estimator, online updating approach, statistical inference, VIX prediction

中图分类号:

O212.7

陈子玉, 郭潇. 关于大数据下非参数平滑化在线更新方法的推断[J]. 中国科学技术大学学报, 2021, 51(5): 390-403.

CHEN Ziyu, GUO Xiao. Inference of online updating approach to nonparametric smoothing of big data[J]. Journal of University of Science and Technology of China, 2021, 51(5): 390-403.

参考文献

[1] Aggarwal C C. Data Streams:Models and Algorithms. Heidelberg: Springer Science & Business Media, 2007.
[2] Aggarwal C C, Yu P S. A Survey of Synopsis Construction in Data Streams. Heidelberg: Springer Science & Business Media, 2007.
[3] Wrench C, Stahl F, Fatta G, et al. Data stream mining of event and complex event streams: A survey of existing and future technologies and applications in big data. In: Enterprise Big Data Engineering, Analytics, and Management. Hershey, PA: IGI Global, 2016.
[4] Cao Y, He H, Man H. SOMKE: Kernel density estimation over data streams by sequences of self-organizing maps. IEEE Transactions on Neural Networks Learning Systems, 2012, 23(8): 1254-1268.
[5] Min X, Ishibuchi H, Xin G, et al. Dm-KDE: Dynamical kernel density estimation by sequences of KDE estimators with fixed number of components over data streams. Frontiers of Computer Science, 2014, 8(4): 563-580.
[6] Fan J, Gijbels I. Local Polynomial Modelling and Its Applications. Boca Raton, FL: CRC Press, 1996.
[7] Härdle W. Applied Nonparametric Regression. Cambridge, UK: Cambridge University Press, 1990.
[8] Härdle W, Linton O. Nonparametric regression. SFB Discussion Papers, 1995, 3(2): 867-877.
[9] Elizabeth S D, Wu J, Wang C, et al. Online updating of statistical inference in the big data setting. Technometrics, 2016, 58(3): 393-403.
[10] Han B, Comaniciu D, Zhu Y, et al. Sequential kernel density approximation and its application to real-time visual tracking. IEEE Transactions on Pattern Analysis Machine Intelligence, 2008, 30(7): 1186-1197.
[11] Spurek P, Byrski K, Tabor J. Online updating of active function cross-entropy clustering. Pattern Analysis and Applications, 2019, 22(4): 1409-1425.
[12] Kong E, Xia Y. On the efficiency of online approach to nonparametric smoothing of big data. Statistica Sinica, 2019, 29(1): 185-201.
[13] Deheuvels P. Estimation nonparamétrique de la densité par histogrammes généralisés. Revue de Statistique Appliquée, 1977, 25(3): 5-42.
[14] Stone M. Cross-validation and multinomial prediction. Biometrika, 1974, 61(3): 509-515.
[15] Cao R, Cuevas A, Manteiga W G. A comparative study of several smoothing methods in density estimation. Computational Statistics Data Analysis, 1994, 17(2): 153-176.
[16] Woodroofe M. On choosing a delta-sequence. Annals of Mathematical Statistics, 1970, 41(5): 1665-1671.
[17] Scott D W, Tapia R A, Thompson J R. Kernel density estimation revisited. Nonlinear Analysis Theory Methods Applications, 1977, 1(4): 339-372.
[18] Cwik J, Koronacki J. A combined adaptive-mixtures/plug-in estimator of multivariate probability densities. Computational Statistics & Data Analysis, 1997, 26(2): 199-218.
[19] Vincent P, Bengio Y. Non-local manifold Parzen windows. In: Advances in Neural Information Processing Systems 15. Cambridge, MA: MIT Press, 2003: 849-856.
[20] Whaley R E. Understanding the VIX. The Journal of Portfolio Management, 2009, 35(3): 98-105.
[21] Jiang G J, Tian Y S. Extracting model-free volatility from option prices: An examination of the VIX index. The Journal of Derivatives, 2007, 14(3): 35-60.

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

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

编辑推荐

Metrics

本文评价

[1]	胡万宝，胡帅，陈雯雯，崔良武. 多节点修复的代数几何码[J]. 中国科学技术大学学报, 2020, 50(2): 140-145.
[2]	徐华，李京. 面向带宽保障的云中虚拟集群调度算法[J]. 中国科学技术大学学报, 2018, 48(6): 495-503.
[3]	周东, 孙玉发, 胡少启, 杨明, 刘伟伟. 一种带宽展宽的圆极化微带天线的设计[J]. 中国科学技术大学学报, 2015, 45(7): 582-587.
[4]	李美莲. 基于模型参数辨识的网络化系统控制策略[J]. 中国科学技术大学学报, 2014, 44(7): 618-622.