Testing Predictor Significance with Ultra High Dimensional Multivariate Responses

29 Pages Posted: 3 Dec 2014

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: December 3, 2014

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 Because the response dimension is ultra high, the classical method of likelihood ratio test is no longer applicable.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 decompose 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.

Keywords: Hypotheses Testing; Multivariate Regression; Paid Search Advertising; Ultra High Dimensional Data

JEL Classification: C3

Suggested Citation

Ma, Yingying and Lan, Wei and Wang, Hansheng, Testing Predictor Significance with Ultra High Dimensional Multivariate Responses (December 3, 2014). Available at SSRN: https://ssrn.com/abstract=2533353 or http://dx.doi.org/10.2139/ssrn.2533353

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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