Improvement of the quality of the chi-square approximation for the ADF test on a covariance matrix with a linear structure
Improvement of the quality of the chi-square approximation for the ADF test on a covariance matrix with a linear structure
复制标题
DOI：
10.1016/j.jspi.2010.11.012
复制
发表时间：
2011-04-01
影响因子：
0.9
通讯作者：
Wakaki, H.
中科院分区：
文献类型：
--
作者：
Matsumoto, C.;Yanagihara, H.;Wakaki, H.
渐近无分布（ADF）检验统计量由 Browne（1984）提出。已知ADF检验统计量的零分布是根据卡方分布渐近分布的。即使在非正态性下，也始终满足这种渐近性质，尽管其他著名检验统计量（例如最大似然检验统计量和广义最小二乘检验统计量）的零分布在非正态性下不会收敛到卡方分布。然而，许多作者报告的数值结果表明，即使样本量很大并且总体分布呈正态，ADF 检验的卡方近似的质量也很差。在本文中，我们尝试通过使用正态性假设下适用的 Bartlett 校正来提高具有线性结构的协方差矩阵的 ADF 检验的卡方近似的质量。通过进行数值研究，我们验证了即使违反正态性假设，所获得的 Bartlett 校正也能表现良好。 (C) 2010 Elsevier B.V. 保留所有权利。
The asymptotically distribution-free (ADF) test statistic was proposed by Browne (1984). It is known that the null distribution of the ADF test statistic is asymptotically distributed according to the chi-square distribution. This asymptotic property is always satisfied, even under nonnormality, although the null distributions of other famous test statistics, e.g., the maximum likelihood test statistic and the generalized least square test statistic, do not converge to the chi-square distribution under nonnormality. However, many authors have reported numerical results which indicate that the quality of the chi-square approximation for the ADF test is very poor, even when the sample size is large and the population distribution is normal. In this paper, we try to improve the quality of the chi-square approximation to the ADF test for a covariance matrix with a linear structure by using the Bartlett correction applicable under the assumption of normality. By conducting numerical studies, we verify that the obtained Bartlett correction can perform well even when the assumption of normality is violated. (C) 2010 Elsevier B.V. All rights reserved.