A simple test of completeness in a class of nonparametric specification
针对一类加性独立误差的非参数位置族，提出检验其完备性的方法，通过检验误差特征函数有无零点来判断，适用于工具变量非参数回归和非经典测量误差模型，并给出渐近性质和蒙特卡洛模拟结果。
This paper provides a test for completeness in a class of nonparametric specification with an additive and independent error term. It is known that such a nonparametric location family of functions is complete if and only if the characteristic function of the error term has no zeros on the real line. Because a zero of the error characteristic function implies that of an observed marginal distribution, we propose a simple test for zeros of characteristic function of the observed distribution, in which rejection of the null hypothesis implies the completeness. This test is applicable to many popular settings, such as nonparametric regression models with instrumental variables, and nonclassical measurement error models. We describe the asymptotic behavior of the tests under the null and alternative hypotheses and investigate the finite sample properties of the proposed test through a Monte Carlo study. We illustrate our method empirically by estimating a measurement error model using the CPS/SSR 1978 exact match file.