The Experts below are selected from a list of 126 Experts worldwide ranked by ideXlab platform
Jianfeng Yao - One of the best experts on this subject based on the ideXlab platform.
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Substitution Principle for clt of linear spectral statistics of high dimensional sample covariance matrices with applications to hypothesis testing
Annals of Statistics, 2015Co-Authors: Shurong Zheng, Zhidong Bai, Jianfeng YaoAbstract:Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLTs) for linear spectral statistics of high-dimensional noncentralized sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for noncentralized sample covariance matrices, some of which even assume Gaussian-like moment conditions. In fact, there are still another two most frequently used sample covariance matrices: the ME (moment estimator, constructed by subtracting the sample mean vector from each sample vector) and the unbiased sample covariance matrix (by changing the denominator $n$ as $N=n-1$ in the ME) without depending on unknown population mean vectors. In this paper, we not only establish the new CLTs for noncentralized sample covariance matrices when the Gaussian-like moment conditions do not hold but also characterize the nonnegligible differences among the CLTs for the three classes of high-dimensional sample covariance matrices by establishing a Substitution Principle: by substituting the adjusted sample size $N=n-1$ for the actual sample size $n$ in the centering term of the new CLTs, we obtain the CLT of the unbiased sample covariance matrices. Moreover, it is found that the difference between the CLTs for the ME and unbiased sample covariance matrix is nonnegligible in the centering term although the only difference between two sample covariance matrices is a normalization by $n$ and $n-1$, respectively. The new results are applied to two testing problems for high-dimensional covariance matrices.
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Substitution Principle for clt of linear spectral statistics of high dimensional sample covariance matrices with applications to hypothesis testing
arXiv: Methodology, 2014Co-Authors: Shurong Zheng, Zhidong Bai, Jianfeng YaoAbstract:Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for non-centered sample covariance matrices, some of which even assume Gaussian-like moment conditions. In fact, there are still another two most frequently used sample covariance matrices: the MLE (by subtracting the sample mean vector from each sample vector) and the unbiased sample covariance matrix (by changing the denominator $n$ as $N=n-1$ in the MLE) without depending on unknown population mean vectors. In this paper, we not only establish new CLT's for non-centered sample covariance matrices without Gaussian-like moment conditions but also characterize the non-negligible differences among the CLT's for the three classes of high-dimensional sample covariance matrices by establishing a {\em Substitution Principle}: substitute the {\em adjusted} sample size $N=n-1$ for the actual sample size $n$ in the major centering term of the new CLT's so as to obtain the CLT of the unbiased sample covariance matrices. Moreover, it is found that the difference between the CLT's for the MLE and unbiased sample covariance matrix is non-negligible in the major centering term although the two sample covariance matrices only have differences $n$ and $n-1$ on the dominator. The new results are applied to two testing problems for high-dimensional data.
Francesco Oliveri - One of the best experts on this subject based on the ideXlab platform.
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exact solutions to the equations of ideal gas dynamics by means of the Substitution Principle
International Journal of Non-linear Mechanics, 1998Co-Authors: Francesco Oliveri, Maria Paola SpecialeAbstract:Abstract In this paper the equations governing three-dimensional unsteady flows of an inviscid, thermally non-conducting fluid, subjected to no extraneous force, are considered. First, some simple exact solutions are explicitly determined; then, by using the invariance of the given equations with respect to a generalized stretching group of all but space variables and a generalized time translation new solutions are immediately constructed. This invariance is known in the literature as Substitution Principle, since it allows to generate new solutions (substituted flows) from given solutions.
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galilean quasilinear systems of pde s and the Substitution Principle
1993Co-Authors: Francesco OliveriAbstract:The quasilinear systems of partial differential equations which are invariant with respect to the celebrated Galilean group of transformations are characterized by means of Lie group analysis. Furthermore, the invariance with respect to a generalized stretching group combined with a generalized time translation is imposed and the conditions for the validity of a Substitution Principle for such kind of systems are easily derived. The results are specialized to the case of the 3D equations of ideal gas-dynamics.
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on the equations of ideal gas dynamics with a separable equation of state lie group analysis and Substitution Principles
International Journal of Non-linear Mechanics, 1992Co-Authors: Francesco OliveriAbstract:Abstract In this paper we consider the equations that govern the flow of an inviscid, thermally non-conducting fluid with a separable equation of state within the theoretical framework of Lie group analysis. We show that the result known in the literature as the Substitution Principle can be derived by suitably imposing the invariance of the basic equations under a one-parameter Lie group of transformations. Moreover, we prove that the use of the Lie group approach leads to different generalizations of the Substitution Principle.
Shurong Zheng - One of the best experts on this subject based on the ideXlab platform.
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Substitution Principle for clt of linear spectral statistics of high dimensional sample covariance matrices with applications to hypothesis testing
Annals of Statistics, 2015Co-Authors: Shurong Zheng, Zhidong Bai, Jianfeng YaoAbstract:Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLTs) for linear spectral statistics of high-dimensional noncentralized sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for noncentralized sample covariance matrices, some of which even assume Gaussian-like moment conditions. In fact, there are still another two most frequently used sample covariance matrices: the ME (moment estimator, constructed by subtracting the sample mean vector from each sample vector) and the unbiased sample covariance matrix (by changing the denominator $n$ as $N=n-1$ in the ME) without depending on unknown population mean vectors. In this paper, we not only establish the new CLTs for noncentralized sample covariance matrices when the Gaussian-like moment conditions do not hold but also characterize the nonnegligible differences among the CLTs for the three classes of high-dimensional sample covariance matrices by establishing a Substitution Principle: by substituting the adjusted sample size $N=n-1$ for the actual sample size $n$ in the centering term of the new CLTs, we obtain the CLT of the unbiased sample covariance matrices. Moreover, it is found that the difference between the CLTs for the ME and unbiased sample covariance matrix is nonnegligible in the centering term although the only difference between two sample covariance matrices is a normalization by $n$ and $n-1$, respectively. The new results are applied to two testing problems for high-dimensional covariance matrices.
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Substitution Principle for clt of linear spectral statistics of high dimensional sample covariance matrices with applications to hypothesis testing
arXiv: Methodology, 2014Co-Authors: Shurong Zheng, Zhidong Bai, Jianfeng YaoAbstract:Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for non-centered sample covariance matrices, some of which even assume Gaussian-like moment conditions. In fact, there are still another two most frequently used sample covariance matrices: the MLE (by subtracting the sample mean vector from each sample vector) and the unbiased sample covariance matrix (by changing the denominator $n$ as $N=n-1$ in the MLE) without depending on unknown population mean vectors. In this paper, we not only establish new CLT's for non-centered sample covariance matrices without Gaussian-like moment conditions but also characterize the non-negligible differences among the CLT's for the three classes of high-dimensional sample covariance matrices by establishing a {\em Substitution Principle}: substitute the {\em adjusted} sample size $N=n-1$ for the actual sample size $n$ in the major centering term of the new CLT's so as to obtain the CLT of the unbiased sample covariance matrices. Moreover, it is found that the difference between the CLT's for the MLE and unbiased sample covariance matrix is non-negligible in the major centering term although the two sample covariance matrices only have differences $n$ and $n-1$ on the dominator. The new results are applied to two testing problems for high-dimensional data.
Maria Paola Speciale - One of the best experts on this subject based on the ideXlab platform.
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exact solutions to the equations of ideal gas dynamics by means of the Substitution Principle
International Journal of Non-linear Mechanics, 1998Co-Authors: Francesco Oliveri, Maria Paola SpecialeAbstract:Abstract In this paper the equations governing three-dimensional unsteady flows of an inviscid, thermally non-conducting fluid, subjected to no extraneous force, are considered. First, some simple exact solutions are explicitly determined; then, by using the invariance of the given equations with respect to a generalized stretching group of all but space variables and a generalized time translation new solutions are immediately constructed. This invariance is known in the literature as Substitution Principle, since it allows to generate new solutions (substituted flows) from given solutions.
Zhidong Bai - One of the best experts on this subject based on the ideXlab platform.
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Substitution Principle for clt of linear spectral statistics of high dimensional sample covariance matrices with applications to hypothesis testing
Annals of Statistics, 2015Co-Authors: Shurong Zheng, Zhidong Bai, Jianfeng YaoAbstract:Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLTs) for linear spectral statistics of high-dimensional noncentralized sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for noncentralized sample covariance matrices, some of which even assume Gaussian-like moment conditions. In fact, there are still another two most frequently used sample covariance matrices: the ME (moment estimator, constructed by subtracting the sample mean vector from each sample vector) and the unbiased sample covariance matrix (by changing the denominator $n$ as $N=n-1$ in the ME) without depending on unknown population mean vectors. In this paper, we not only establish the new CLTs for noncentralized sample covariance matrices when the Gaussian-like moment conditions do not hold but also characterize the nonnegligible differences among the CLTs for the three classes of high-dimensional sample covariance matrices by establishing a Substitution Principle: by substituting the adjusted sample size $N=n-1$ for the actual sample size $n$ in the centering term of the new CLTs, we obtain the CLT of the unbiased sample covariance matrices. Moreover, it is found that the difference between the CLTs for the ME and unbiased sample covariance matrix is nonnegligible in the centering term although the only difference between two sample covariance matrices is a normalization by $n$ and $n-1$, respectively. The new results are applied to two testing problems for high-dimensional covariance matrices.
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Substitution Principle for clt of linear spectral statistics of high dimensional sample covariance matrices with applications to hypothesis testing
arXiv: Methodology, 2014Co-Authors: Shurong Zheng, Zhidong Bai, Jianfeng YaoAbstract:Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for non-centered sample covariance matrices, some of which even assume Gaussian-like moment conditions. In fact, there are still another two most frequently used sample covariance matrices: the MLE (by subtracting the sample mean vector from each sample vector) and the unbiased sample covariance matrix (by changing the denominator $n$ as $N=n-1$ in the MLE) without depending on unknown population mean vectors. In this paper, we not only establish new CLT's for non-centered sample covariance matrices without Gaussian-like moment conditions but also characterize the non-negligible differences among the CLT's for the three classes of high-dimensional sample covariance matrices by establishing a {\em Substitution Principle}: substitute the {\em adjusted} sample size $N=n-1$ for the actual sample size $n$ in the major centering term of the new CLT's so as to obtain the CLT of the unbiased sample covariance matrices. Moreover, it is found that the difference between the CLT's for the MLE and unbiased sample covariance matrix is non-negligible in the major centering term although the two sample covariance matrices only have differences $n$ and $n-1$ on the dominator. The new results are applied to two testing problems for high-dimensional data.
