The Experts below are selected from a list of 4929 Experts worldwide ranked by ideXlab platform
Zhidong Bai - One of the best experts on this subject based on the ideXlab platform.
-
Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix
The Annals of Statistics, 2013Co-Authors: Ningning Xia, Yingli Qin, Zhidong BaiAbstract: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.
-
convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix
Annals of Statistics, 2013Co-Authors: Ningning Xia, Yingli Qin, Zhidong BaiAbstract: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 Mary cenko– 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 η> 0, the convergence rates of VESD are O(N −1/4 ) in probability and O(N −1/4+η ) almost surely, requiring finite 8th moment of the underlying distribution.
Ningning Xia - One of the best experts on this subject based on the ideXlab platform.
-
Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix
The Annals of Statistics, 2013Co-Authors: Ningning Xia, Yingli Qin, Zhidong BaiAbstract: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.
-
convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix
Annals of Statistics, 2013Co-Authors: Ningning Xia, Yingli Qin, Zhidong BaiAbstract: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 Mary cenko– 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 η> 0, the convergence rates of VESD are O(N −1/4 ) in probability and O(N −1/4+η ) almost surely, requiring finite 8th moment of the underlying distribution.
Yingli Qin - One of the best experts on this subject based on the ideXlab platform.
-
Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix
The Annals of Statistics, 2013Co-Authors: Ningning Xia, Yingli Qin, Zhidong BaiAbstract: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.
-
convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix
Annals of Statistics, 2013Co-Authors: Ningning Xia, Yingli Qin, Zhidong BaiAbstract: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 Mary cenko– 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 η> 0, the convergence rates of VESD are O(N −1/4 ) in probability and O(N −1/4+η ) almost surely, requiring finite 8th moment of the underlying distribution.
E.c. Van Der Meulen - One of the best experts on this subject based on the ideXlab platform.
-
Minimum Kolmogorov Distance Estimates for Multivariate Parametrized Families
American Journal of Mathematical and Management Sciences, 1996Co-Authors: László Györfi, I. Vajda, E.c. Van Der MeulenAbstract:SYNOPTIC ABSTRACTIn a previous paper we introduced minimum Kolmogorov Distance estimates of distribution parameters and distribution densities for arbitrarily parametrized univariate statistical models. This paper is an extension to the multivariate case. Some results extend straightforwardly, the extension of other ones is quite difficult. It is shown that the Kolmogorov Distance parameter estimates are strongly consistent if the parameter space metric is topologically weaker than the metric induced by the Kolmogorov Distance of distributions from the statistical model. If the parameter space metric is locally uniformly bounded above by the induced metric then the estimates are consistent of order n−½ Similar results are proved for the Kolmogorov Distance estimates of densities from parametrized families. In this case the consistency is considered in the L1-norm.
-
Minimum Kolmogorov Distance estimates of parameters and parametrized distributions
Metrika, 1996Co-Authors: László Györfi, I. Vajda, E.c. Van Der MeulenAbstract:Minimum Kolmogorov Distance estimates of arbitrary parameters are considered. They are shown to be strongly consistent if the parameter space metric is topologically weaker than the metric induced by the Kolmogorov Distance of distributions from the statistical model. If the parameter space metric can be locally uniformly upper-bounded by the induced metric then these estimates are shown to be consistent of ordern−1/2. Similar results are proved for minimum Kolmogorov Distance estimates of densities from parametrized families where the consistency is considered in theL1-norm. The presented conditions for the existence, consistency, and consistency of ordern−1/2 are much weaker than those established in the literature for estimates with similar properties. It is shown that these assumptions are satisfied e.g. by all location and scale models with parent distributions different from Dirac, and by all standard exponential models.
László Györfi - One of the best experts on this subject based on the ideXlab platform.
-
Minimum Kolmogorov Distance Estimates for Multivariate Parametrized Families
American Journal of Mathematical and Management Sciences, 1996Co-Authors: László Györfi, I. Vajda, E.c. Van Der MeulenAbstract:SYNOPTIC ABSTRACTIn a previous paper we introduced minimum Kolmogorov Distance estimates of distribution parameters and distribution densities for arbitrarily parametrized univariate statistical models. This paper is an extension to the multivariate case. Some results extend straightforwardly, the extension of other ones is quite difficult. It is shown that the Kolmogorov Distance parameter estimates are strongly consistent if the parameter space metric is topologically weaker than the metric induced by the Kolmogorov Distance of distributions from the statistical model. If the parameter space metric is locally uniformly bounded above by the induced metric then the estimates are consistent of order n−½ Similar results are proved for the Kolmogorov Distance estimates of densities from parametrized families. In this case the consistency is considered in the L1-norm.
-
Minimum Kolmogorov Distance estimates of parameters and parametrized distributions
Metrika, 1996Co-Authors: László Györfi, I. Vajda, E.c. Van Der MeulenAbstract:Minimum Kolmogorov Distance estimates of arbitrary parameters are considered. They are shown to be strongly consistent if the parameter space metric is topologically weaker than the metric induced by the Kolmogorov Distance of distributions from the statistical model. If the parameter space metric can be locally uniformly upper-bounded by the induced metric then these estimates are shown to be consistent of ordern−1/2. Similar results are proved for minimum Kolmogorov Distance estimates of densities from parametrized families where the consistency is considered in theL1-norm. The presented conditions for the existence, consistency, and consistency of ordern−1/2 are much weaker than those established in the literature for estimates with similar properties. It is shown that these assumptions are satisfied e.g. by all location and scale models with parent distributions different from Dirac, and by all standard exponential models.
