Enhanced Power Enhancements for Testing Many Moment Equalities: Beyond the 2- and ∞-norm
本文提出一种利用所有p-范数（p∈[2,∞]）的检验方法，比仅基于2-范数和无穷范数的检验能检测更多备择假设，并在多工具变量线性模型中验证了其优势。
Tests based on the 2- and ∞-norm have received considerable attention in high-dimensional testing problems, as they are powerful against dense and sparse alternatives, respectively. The power enhancement principle of Fan et al. (2015) combines these two norms to construct improved tests that are powerful against both types of alternatives. In the context of testing whether a candidate parameter satisfies a large number of moment equalities, we construct tests that harness the strength of all p-norms with p∈[2,∞]. As a result, these tests are consistent against strictly more alternatives than any test based on a single p-norm. In particular, our tests are consistent against more alternatives than tests based on the 2- and ∞-norm, which is what most implementations of the power enhancement principle target.We illustrate our general results in the linear instrumental variable model with many instruments, for which we also provide numerical results and an empirical illustration.