Factor and Idiosyncratic Empirical Processes

• Activity Number: 81 - Regression, Distribution and Inference
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Jiangyan Wang* and Xinbing Kong and Jinbao Xing and Chao Xu and Chao Ying
• Companies: Nanjing Audit University and Nanjing Audit University and Soochow University and Nanjing Audit University and Soochow University
• Keywords: : Factor model; ; Empirical process; Principal component analysis; Simultaneous confidence band

Abstract

Using the recently developed theory for large dimensional approximate factor model for large panel data, the common and idiosyncratic components can be estimated consistently. Based on the estimated common and idiosyncratic components, we construct the empirical processes for estimation of the distribution functions of the common and idiosyncratic components. 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 idiosyncratic empirical processes behave as well as the empirical processes pretending that the common and idiosyncratic components for an individual variable are directly observable. Based on this oracle property, we construct simultaneous confidence bands (SCBs) for the distributions of the common and idiosyncratic components. For the first-order consistency of the estimated distribution functions, ?T = o(p) suffices. Extensive simulation studies check that the estimated bands have good coverage frequencies.