The limits of the sample spiked eigenvalues for a high-dimensional generalized Fisher matrix and its applications.
@article{Jiang2019TheLO, title={The limits of the sample spiked eigenvalues for a high-dimensional generalized Fisher matrix and its applications.}, author={Dandan Jiang and Jiang Hu and Zhiqiang Hou}, journal={arXiv: Statistics Theory}, year={2019} }
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References
SHOWING 1-10 OF 29 REFERENCES
ASYMPTOTICS OF SAMPLE EIGENSTRUCTURE FOR A LARGE DIMENSIONAL SPIKED COVARIANCE MODEL
- Mathematics
- 2007
This paper deals with a multivariate Gaussian observation model where the eigenvalues of the covariance matrix are all one, except for a finite number which are larger. Of interest is the asymptotic…
Central limit theorems for eigenvalues in a spiked population model
- Mathematics
- 2008
In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with…
Generalized four moment theorem and an application to CLT for spiked eigenvalues of high-dimensional covariance matrices
- Mathematics
- 2018
We consider a more generalized spiked covariance matrix $\Sigma$, which is a general non-definite matrix with the spiked eigenvalues scattered into a few bulks and the largest ones allowed to tend to…
Limiting laws for divergent spiked eigenvalues and largest nonspiked eigenvalue of sample covariance matrices
- MathematicsThe Annals of Statistics
- 2020
We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance matrix model with divergent spiked…
On sample eigenvalues in a generalized spiked population model
- MathematicsJ. Multivar. Anal.
- 2012
Asymptotics of Empirical Eigen-structure for Ultra-high Dimensional Spiked Covariance Model
- Computer Science
- 2015
These results are a natural extension of those in Paul (2007) to more general setting with new insights and solve the rates of convergence problems in Shen et al. (2013), and reveal the biases of the estimation of leading eigenvalues and eigenvectors by using principal component analysis.
Asymptotics of empirical eigenstructure for high dimensional spiked covariance.
- MathematicsAnnals of statistics
- 2017
These results are a natural extension of those in Paul (2007) to a more general setting and solve the rates of convergence problems in Shen et al. (2013) and lead to a new covariance estimator for the approximate factor model, called shrinkage principal orthogonal complement thresholding (S-POET), that corrects the biases.
CLT for eigenvalue statistics of large-dimensional general Fisher matrices with applications
- Mathematics, Computer Science
- 2017
The limiting distribution of the eigen values of a general Fisher matrix is found and a central limit theorem is established for a wide class of functionals of these eigenvalues.
CLT for large dimensional general Fisher matrices and its applications in high-dimensional data analysis
- Mathematics, Computer Science
- 2014
The first main result of the paper establishes the limiting distribution of the eigenvalues of a Fisher matrix while in a second main result, the central limit theorem is provided for a wide class of functionals of its eigen values.