Efficient Tests Under a Weak Convergence Assumption
以数据函数的弱收敛为起点，研究在相同弱极限下所有渐近有效检验中的效率问题，发现有效检验可由极限问题中的有效检验代入样本对应量得到，为计量经济学中许多已有检验（如单位根检验、参数稳定性检验）提供了更广泛的渐近效率意义。
The asymptotic validity of tests is usually established by making appropriate primitive assumptions, which imply the weak convergence of a specific function of the data, and an appeal to the continuous mapping theorem.This paper, instead, takes the weak convergence of some function of the data to a limiting random element as the starting point and studies efficiency in the class of tests that remain asymptotically valid for all models that induce the same weak limit.It is found that efficient tests in this class are simply given by efficient tests in the limiting problem-that is, with the limiting random element assumed observed-evaluated at sample analogues.Efficient tests in the limiting problem are usually straightforward to derive, even in nonstandard testing problems.What is more, their evaluation at sample analogues typically yields tests that coincide with suitably robustified versions of optimal tests in canonical parametric versions of the model.This paper thus establishes an alternative and broader sense of asymptotic efficiency for many previously derived tests in econometrics, such as tests for unit roots, parameter stability tests, and tests about regression coefficients under weak instruments.