تقرير
Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix
| العنوان: | Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix |
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| المؤلفون: | Xia, Ningning, Qin, Yingli, Bai, Zhidong |
| المصدر: | Annals of Statistics 2013, Vol. 41, No. 5, 2572-2607 |
| سنة النشر: | 2013 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory |
| الوصف: | The eigenvector Empirical Spectral Distribution (VESD) is adopted to investigate the limiting behavior of eigenvectors and eigenvalues of covariance matrices. In this paper, we shall show that the Kolmogorov distance between the expected VESD of sample covariance matrix and the Mar\v{c}enko-Pastur distribution function is of order $O(N^{-1/2})$. Given that data dimension $n$ to sample size $N$ ratio is bounded between 0 and 1, this convergence rate is established under finite 10th moment condition of the underlying distribution. It is also shown that, for any fixed $\eta>0$, the convergence rates of VESD are $O(N^{-1/4})$ in probability and $O(N^{-1/4+\eta})$ almost surely, requiring finite 8th moment of the underlying distribution. Comment: Published in at http://dx.doi.org/10.1214/13-AOS1154 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1214/13-AOS1154 |
| URL الوصول: | http://arxiv.org/abs/1311.5000 |
| رقم الأكسشن: | edsarx.1311.5000 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1214/13-AOS1154 |
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