講座題目：Factor and idiosyncratic empirical processes
主 講 人：孔新兵
時 間：3月30日（周五）下午14:30
地 點：燕山校區一號教學樓統計學院資料室
主 辦：科研處、統計學院（大數據與指數研究院）、山東省大數據研究會
報告摘要：
The distributions of the factor return and specific error for an individual variable are important in forecasting and applications. However, they are not identified with low dimensional observations. Using the recently developed theory for large dimensional approximate factor model for large panel data, the factor return and specific error can be estimated consistently. Based on the estimated factor returns and residual errors, we construct the empirical processes for estimation of the distribution functions of the factor return and specific error, respectively. We prove that the two empirical processes are oracle efficient when $T=o(p)$ where $p$ and $T$ are the dimension and sample size, respectively. This demonstrates that the factor and residual empirical processes behave as well as the empirical processes pretending that the factor returns and specific errors for an individual variable are directly observable. Based on this oracle property, we construct simultaneous confidence bands (SCBs) for the distributions of the factor return and specific error. For the first order consistency of the estimated factor and residual distributions, $\sqrt{T}=o(p)$ suffices. Extensive simulation studies check that the estimated bands have good coverage frequencies. Our real data analysis shows that the factor return distribution has a structural change during the crisis in 2008, while the idiosyncratic return distribution does not change much.
主講人簡介：
孔新兵，南京審計大學、統計與數學學院/統計與大數據研究院、教授。2011年7月-2014年7月，復旦大學管理學院助理教授及副教授。2014年8月-2017年2月，蘇州大學數學學院及高等統計與計量經濟研究中心教授。孔新兵教授博士畢業于香港科技大學，目前的研究領域為經濟統計、數理統計、網絡數據統計，在統計學頂級期刊Annals of Statistics, Journal of the American Statistical Association, Biometrika 以及計量經濟學頂級期刊 Journal of Econometric, Journal of Business and Economic Statistics 發表多篇研究論文。孔新兵教授目前為國際統計協會(ISI)會員，現場統計研究會高維統計分會理事，江蘇省“雙創博士”，曾獲香港數學會“最佳博士論文獎”，復旦大學管理學院年度“青年新星獎”等，主持多項國家自然科學基金以及教育部人文社科基金。
