Abstract

The density function of the limiting spectral distribution(LSD) of sample covariance matrices is widely used in large scale statistical inference when the sample size and dimension both tend to infinity. However, there are no explicit expressions for the density function generated by vector autoregressive moving average(VARMA) models. For such models whose sample covariance matrices do not have independence structure in columns, we propose to use modified kernel estimators which are proved to be consistent. A simulation study is also conducted to show the performance of the estimators.

中文翻译：

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VARMA 模型生成的样本协方差矩阵的谱密度函数的非参数估计

摘要

样本协方差矩阵的极限谱分布(LSD)密度函数广泛应用于样本量和维数均趋于无穷大的大规模统计推断中。然而，向量自回归移动平均（VARMA）模型生成的密度函数没有明确的表达式。对于样本协方差矩阵在列中没有独立结构的此类模型，我们建议使用已证明是一致的修改后的核估计器。还进行了模拟研究以显示估计器的性能。