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A high dimensional two-sample test under a low dimensional factor structure

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  • Ma, Yingying
  • Lan, Wei
  • Wang, Hansheng

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.

Suggested Citation

  • Ma, Yingying & Lan, Wei & Wang, Hansheng, 2015. "A high dimensional two-sample test under a low dimensional factor structure," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 162-170.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:162-170
    DOI: 10.1016/j.jmva.2015.05.005
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    References listed on IDEAS

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    Cited by:

    1. Zhang, Jin-Ting & Guo, Jia & Zhou, Bu, 2017. "Linear hypothesis testing in high-dimensional one-way MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 200-216.
    2. Wang, Rui & Xu, Xingzhong, 2018. "On two-sample mean tests under spiked covariances," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 225-249.
    3. Mingxiang Cao & Yuanjing He, 2022. "A high-dimensional test on linear hypothesis of means under a low-dimensional factor model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 557-572, July.
    4. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.
    5. Ma, Yingying & Lan, Wei & Zhou, Fanying & Wang, Hansheng, 2020. "Approximate least squares estimation for spatial autoregressive models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    6. Hyodo, Masashi & Nishiyama, Takahiro & Pavlenko, Tatjana, 2023. "A Behrens–Fisher problem for general factor models in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    7. Zhang, Jin-Ting & Zhou, Bu & Guo, Jia, 2022. "Linear hypothesis testing in high-dimensional heteroscedastic one-way MANOVA: A normal reference L2-norm based test," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    8. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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