NEYMAN’S C(α) TEST FOR UNOBSERVED HETEROGENEITY
提出基于奈曼C(α)方法的统一框架，检验参数统计模型中的未观测异质性，适用于多维情况，可改进现有检验的势。
A unified framework is proposed for tests of unobserved heterogeneity in parametric statistic models based on Neyman’s C( α ) approach. Such tests are irregular in the sense that the first order derivative of the log likelihood with respect to the heterogeneity parameter is identically zero, and consequently the conventional Fisher information about the parameter is zero. Nevertheless, local asymptotic optimality of the C( α ) tests can be established via LeCam’s differentiability in quadratic mean and the limit experiment approach. This leads to local alternatives of order n −1/4 . The scalar case result is already familiar from existing literature and we extend it to the multidimensional case. The new framework reveals that certain regularity conditions commonly employed in earlier developments are unnecessary, i.e. the symmetry or third moment condition imposed on the heterogeneity distribution. Additionally, the limit experiment for the multidimensional case suggests modifications on existing tests for slope heterogeneity in cross sectional and panel data models that lead to power improvement. Since the C( α ) framework is not restricted to the parametric model and the test statistics do not depend on the particular choice of the heterogeneity distribution, it is useful for a broad range of applications for testing parametric heterogeneity.