  We propose a novel technique to boost the power of testing a high-dimensional
vector $H:\btheta=0$ 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 a byproduct, the
power enhancement component also consistently identifies the elements that
violate the null hypothesis. As specific applications, the proposed methods are
applied to testing the factor pricing models and validating the cross-sectional
independence in panel data models.
