Asymptotic Theory for Sample Covariance Matrix under Cross – Sectional Dependence
Asymptotic Theory for Sample Covariance Matrix under Cross – Sectional Dependence
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发表时间：
2010
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通讯作者：
G. Pan;Jiti Gao
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作者：
G. Pan;Jiti Gao
当p→∞和n→∞且pn→0时，证明了其经验谱分布在第四矩条件下收敛于固定分布。然后讨论了这样的渐近分布可用于推导截面独立性假设检验的渐近一致检验。
where X = (Xij)p×n consists of independent and identically distributed real random variables and T is a symmetric nonnegative definite nonrandom matrix. When p → ∞ and n → ∞ with p n → 0, it is shown that its empirical spectral distribution converges to a fixed distribution under the fourth moment condition. It is then discussed that such an asymptotic distribution can be used to derive an asymptotically consistent test for the hypothesis testing of cross–sectional independence.