Longbing Cao

Publications (4)0 Total impact

• Article: Asymptotic power of likelihood ratio tests for high dimensional data

  Cheng Wang, Longbing Cao, Baiqi Miao
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  ABSTRACT: This paper considers the asymptotic power of likelihood ratio test (LRT) for the identity test when the dimension p is large compared to the sample size n. The asymptotic distribution of LRT under alternatives is given and an explicit expression of the power is derived. A simulation study is carried out to compare LRT with other tests. All these studies show that LRT is a powerful test to detect eigenvalues around zero. Key words and phrases: Covariance matrix, High dimensional data, Identity test, Likelihood ratio test, Power
  02/2013;
• Article: A shrinkage estimation for large dimensional precision matrices using random matrix theory

  Cheng Wang, Guangming Pan, Longbing Cao
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  ABSTRACT: In this work, a new data-driven shrinkage estimator for the population precision matrix has been introduced using random matrix theory. The new estimation is non-parametric without assuming a specific parameter distribution for the data and also there is no prior information about the structure of the population covariance matrix. We demonstrate by both theoretical and empirical studies that the new estimator, which is applicable for p > n, has good properties for a wide range of dimensions and sample sizes. Moreover, even if p < n, our new method always dominates the inverse sample covariance matrix and performs comparably with existing methods.
  11/2012;
• Article: Non-parametric shrinkage mean estimation for arbitrary quadratic loss functions and unknown covariance matrices

  Cheng Wang, Tiejun Tong, Longbing Cao, Baiqi Miao
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  ABSTRACT: In this paper, a shrinkage estimator for the population mean is proposed under arbitrary quadratic loss functions with unknown covariance matrices. The new estimator is non-parametric in the sense that it does not assume a specific parametric distribution for the data and it does not require the prior information on the population covariance matrix. Analytical results on the improvement of the proposed shrinkage estimator are provided and some corresponding asymptotic properties are also derived. Finally, we demonstrate the practical improvement of the proposed method over existing methods through extensive simulation studies and real data analysis. Keywords: High-dimensional data; Shrinkage estimator; Large $p$ small $n$; $U$-statistic.
  11/2012;
• Article: Optimal feature selection for sparse linear discriminant analysis and its applications in gene expression data

  Cheng Wang, Longbing Cao, Baiqi Miao
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  ABSTRACT: This work studies the theoretical rules of feature selection in linear discriminant analysis (LDA), and a new feature selection method is proposed for sparse linear discriminant analysis. An $l_1$ minimization method is used to select the important features from which the LDA will be constructed. The asymptotic results of this proposed two-stage LDA (TLDA) are studied, demonstrating that TLDA is an optimal classification rule whose convergence rate is the best compared to existing methods. The experiments on simulated and real datasets are consistent with the theoretical results and show that TLDA performs favorably in comparison with current methods. Overall, TLDA uses a lower minimum number of features or genes than other approaches to achieve a better result with a reduced misclassification rate.
  06/2012;