Neyman C（α）检验用于未观察到的异质结
Neyman's C(α) Test for Unobserved Heterogeneity
摘要：
基于Neyman的$C(α)$方法，提出了参数统计模型中不可观测异质性检验的统一框架.这样的测试是不规则的，在这个意义上，一阶导数的对数似然相对于异质性参数是相同的零，因此，传统的Fisher信息的参数是零。然而，局部渐近最优性的$C(α)$测试可以建立通过LeCam的可微性在二次均值和极限实验方法。这导致了顺序为$n^{-1/4}$的局部替换。标量的情况下，结果已经从现有的文献中熟悉，我们将其扩展到多维的情况下。新的框架揭示了某些规则性条件通常采用在早期的发展是不必要的，即对称性或三阶矩条件施加在异质性分布。此外，多维情况下的极限实验表明，修改现有的测试斜率异质性的横截面和面板数据模型，导致功率的提高。由于$C(α)$框架不限于参数模型，并且检验统计量不依赖于异质性分布的特定选择，因此它适用于检验参数异质性的广泛应用。
英文摘要：
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 multi-dimensional 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 multi-dimensional 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.
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