Power Enhancement in HighDimensional CrossSectional Tests

Jianqing Fan Yuan Liao Jiawei Yao

Statistics Theory and Methods mathscidoc:1912.43330

Econometrica, 83, (4), 1497-1541, 2015.7
We propose a novel technique to boost the power of testing a highdimensional vector <i>H</i>:<i><b></b></i>=<b>0</b> against sparse alternatives where the null hypothesis is violated by only a few 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 highdimensional 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
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  title={Power Enhancement in HighDimensional CrossSectional Tests},
  author={Jianqing Fan, Yuan Liao, and Jiawei Yao},
Jianqing Fan, Yuan Liao, and Jiawei Yao. Power Enhancement in HighDimensional CrossSectional Tests. 2015. Vol. 83. In Econometrica. pp.1497-1541. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113741475160890.
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