A High Dimensional Two-Sample Test Under a Low Dimensional Factor Structure

22 Pages Posted: 7 Sep 2015

See all articles by Yingying Ma

Yingying Ma

Beihang University (BUAA)

Wei Lan

Peking University - Guanghua School of Management

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: September 7, 2015

Abstract

Existing high dimensional two-sample tests usually assume that different elements of a high dimensional predictor are weakly dependent. Such a condition can be violated when data follow a low dimensional latent factor structure. As a result, the recently developed two-sample testing methods are not directly applicable. To fulfill such a theoretical gap, we propose here a Factor Adjusted two-Sample Testing (FAST) procedure to accommodate the low dimensional latent factor structure. Under the null hypothesis, together with fairly weak technical conditions, we show that the proposed test statistic is asymptotically distributed as a weighted chi-square distribution with a finite number of degrees of freedom. This leads to a totally different test statistic and inference procedure, as compared with those of Bai and Saranadasa (1996) and Chen and Qin (2010). Simulation studies are carried out to examine its finite sample performance. A real example on China stock market is analyzed for illustration purpose.

Keywords: China Stock Market; High-dimensional data; Hypothesis testing; Latent factor structure; Two-Sample Test

JEL Classification: C3

Suggested Citation

Ma, Yingying and Lan, Wei and Wang, Hansheng, A High Dimensional Two-Sample Test Under a Low Dimensional Factor Structure (September 7, 2015). Available at SSRN: https://ssrn.com/abstract=2656961 or http://dx.doi.org/10.2139/ssrn.2656961

Yingying Ma

Beihang University (BUAA) ( email )

37 Xue Yuan Road
Beijing 100083
China

Wei Lan

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

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