An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model Against a Nonparametric Alternative
提出一种新的检验方法，用于检验条件均值函数的参数模型是否成立，该方法能自适应于非参数备择的光滑性，并在备择与参数模型距离以最快可能速率收敛到零时具有一致检验力，蒙特卡洛实验表明其有限样本功效优于现有检验。
We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n -1/2 . Some existing tests have nontrivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n -1/2 . There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finite-sample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.