论文标题
在约翰的大面板数据模型中的球形测试中
On John's test for sphericity in large panel data models
论文作者
论文摘要
本文研究了约翰在大面板数据模型中对误差项的领域测试，其中横截面单元的数量$ n $足够大，可以与次数串联观测值$ t $相当，甚至更大。基于最近的随机矩阵理论结果，约翰测试的渐近态性特性均在零假设和替代假设下建立。这些渐进性对于普通人群有效，即不一定提供某些有限的时刻。本文中发现的一种奇妙的现象是，约翰对面板数据模型的测试具有强大的尺寸属性。 It keeps the same null distribution under different $(n,T)$-asymptotics, i.e., the small or medium panel regime $n/T\to 0$ as $T\to \infty$, the large panel regime $n/T\to c \in (0,\infty)$ as $ T\to \infty$, and the ultra-large panel regime $n/T\to \infty （t^δ/n = o_p（1），1 <δ<2）$ as $ t \ to \ infty $。此外，约翰的测试始终是一致的，除非在有界标记协方差的替代方面与大面板式$ n/t \ to c \ in（0，\ infty）$。
This paper studies John's test for sphericity of the error terms in large panel data models, where the number of cross-section units $n$ is large enough to be comparable to the number of times series observations $T$, or even larger. Based on recent random matrix theory results, John's test's asymptotic normality properties are established under both the null and the alternative hypotheses. These asymptotics are valid for general populations, i.e., not necessarily Gaussian provided certain finite moments. A fantastic phenomenon found in the paper is that John's test for panel data models possesses a powerful dimension-proof property. It keeps the same null distribution under different $(n,T)$-asymptotics, i.e., the small or medium panel regime $n/T\to 0$ as $T\to \infty$, the large panel regime $n/T\to c \in (0,\infty)$ as $ T\to \infty$, and the ultra-large panel regime $n/T\to \infty (T^δ/n =O_p(1), 1<δ<2)$ as $T\to \infty$. Moreover, John's test is always consistent except under the alternative of bounded-norm covariance with the large panel regime $n/T\to c \in (0,\infty)$.
