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Testing predictor significance with ultra high dimensional multivariate responses

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

Abstract

We consider here the problem of testing the effect of a subset of predictors for a regression model with predictor dimension fixed but ultra high dimensional responses. Because the response dimension is ultra high, the classical method of likelihood ratio test is no longer applicable. To solve the problem, we propose a novel solution, which decomposes the original problem into many testing problems with univariate responses. Subsequently, the usual residual sum of squares (RSS) type test statistics can be obtained. Those statistics are then integrated together across different responses to form an overall and powerful test statistic. Under the null hypothesis, the resulting test statistic is asymptotically standard normal after some appropriate standardization. Numerical studies are presented to demonstrate the finite sample performance of the test statistic and a real example about paid search advertising is analyzed for illustration purpose.

Suggested Citation

  • Ma, Yingying & Lan, Wei & Wang, Hansheng, 2015. "Testing predictor significance with ultra high dimensional multivariate responses," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 275-286.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:275-286
    DOI: 10.1016/j.csda.2014.09.020
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    References listed on IDEAS

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    1. Jelle J. Goeman & Sara A. Van De Geer & Hans C. Van Houwelingen, 2006. "Testing against a high dimensional alternative," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 477-493, June.
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    4. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    5. Wei Lan & Hansheng Wang & Chih-Ling Tsai, 2014. "Testing covariates in high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 279-301, April.
    6. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
    7. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    8. Anindya Ghose & Sha Yang, 2009. "An Empirical Analysis of Search Engine Advertising: Sponsored Search in Electronic Markets," Management Science, INFORMS, vol. 55(10), pages 1605-1622, October.
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    Cited by:

    1. Liu, Yang & Sun, Wei & Hsu, Li & He, Qianchuan, 2022. "Statistical inference for high-dimensional pathway analysis with multiple responses," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).

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