Consistency of large dimensional sample covariance matrix under weak dependence

Monika Bhattacharjee; Arup Bose

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Consistency of large dimensional sample covariance matrix under weak dependence

机译：弱相关性下大样本样本协方差矩阵的一致性

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摘要

Convergence rates for banded and tapered estimates of large dimensional covariance matrices are known when the vector observations are independent and identically distributed. We investigate the case where the independence does not hold. Our models can accommodate suitable patterned cross covariance matrices. These estimators remain consistent in the operator norm with appropriate rates of convergence under suitable class of models.

机译：当向量观测值独立且分布均匀时，已知大维协方差矩阵的带状估计和渐缩估计的收敛速度。我们调查独立性不成立的情况。我们的模型可以容纳合适的图案化交叉协方差矩阵。在适当的模型类别下，这些估计量在操作员范本中以适当的收敛速度保持一致。

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来源
《Statistical Methodology》 |2014年第9期|11-26|共16页
作者
Monika Bhattacharjee; Arup Bose;
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作者单位

Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India;

Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India;

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正文语种 eng
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关键词
High-dimensional data; Covariance matrices; Cross covariances; Regularization; Banding; Tapering; Convergence rate; Operator norm;

机译：高维数据;协方差矩阵;交叉协方差;正则化;绑带;锥度收敛速度;运营商规范;

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1. Weak Convergence of the Empirical Spectral Distribution of High-Dimensional Band Sample Covariance Matrices [J] . Jurczak Kamil Journal of theoretical probability . 2018,第3期

机译：高维频带样本协方差矩阵经验谱分布的弱收融
2. HIGH-DIMENSIONAL TWO-SAMPLE COVARIANCE MATRIX TESTING VIA SUPER-DIAGONALS [J] . Jing He, Song Xi Statistica Sinica . 2018,第4aPta2期

机译：通过超级对角线的高维两种协方差矩阵测试
3. HIGH-DIMENSIONAL TWO-SAMPLE COVARIANCE MATRIX TESTING VIA SUPER-DIAGONALS [J] . He Jing, Chen Song Xi Statistica Sinica . 2018,第4aPta1期

机译：通过超级对角线的高维两种协方差矩阵测试
4. Matrix pencil based toeplitz covariance matrix reconstruction approach for correlated weak source detection [C] . Jing Wang, Fei Ji, Fangjiong Chen IEEE International Conference on Signal Processing, Communications and Computing . 2017

机译：基于矩阵铅笔的toeplitz协方差矩阵重构方法用于相关弱源检测
5. High-dimensional structured covariance matrix estimation with financial applications [D] . Mincheva, Martina Zhelcheva 2014

机译：具有金融应用的高维结构化协方差矩阵估计
6. Determining the Effective Dimensionality of the Genetic Variance–Covariance Matrix [O] . Emma Hine, Mark W. Blows 2006

机译：确定遗传方差-协方差矩阵的有效维数
7. On the weak limit of the largest eigenvalue of a large dimensional sample covariance matrix [O] . Silverstein Jack W 1989

机译：大维样本协方差矩阵的最大特征值的弱极限
8. Limit of the Largest Eigenvalue of the Large Dimensional Sample Covariance Matrix [R] . Yin, Y. Q., Bai, Z. D., Krishnaiah, P. R. 1984

机译：大维样本协方差矩阵的最大特征值的极限

Consistency of large dimensional sample covariance matrix under weak dependence

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