Power Enhancement in High Dimensional Cross-Sectional Tests

Econometrica : Journal of the Econometric Society
Jianqing FanJiawei Yao

Abstract

We propose a novel technique to boost the power of testing a high-dimensional vector H : θ = 0 against sparse alternatives where the null hypothesis is violated only by a couple of components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due to the accumulation of errors in estimating high-dimensional parameters. More powerful tests for sparse alternatives such as thresholding and extreme-value tests, on the other hand, require either stringent conditions or bootstrap to derive the null distribution and often suffer from size distortions due to the slow convergence. Based on a screening technique, we introduce a "power enhancement component", which is zero under the null hypothesis with high probability, but diverges quickly under sparse alternatives. The proposed test statistic combines the power enhancement component with an asymptotically pivotal statistic, and strengthens the power under sparse alternatives. The null distribution does not require stringent regularity conditions, and is completely determined by that of the pivotal statistic. As specific applications, the proposed methods are applied to testing the factor pricing models and validating the cross-sectional inde...Continue Reading

Citations

Mar 27, 2018·Journal of the Royal Statistical Society. Series B, Statistical Methodology·Huixia Judy WangMin Qian
Aug 15, 2017·Biometrika·Gongjun XuWei Pan
Aug 21, 2019·Biometrika·Yang LiuQianchuan He
Oct 31, 2018·BMC Genetics·Yujing YaoJoseph H Lee
Dec 4, 2021·Annals of Statistics·Yinqiu HeWei Pan

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