21 research outputs found

    On Identity Tests for High Dimensional Data Using RMT

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    In this work, we redefined two important statistics, the CLRT test (Bai et.al., Ann. Stat. 37 (2009) 3822-3840) and the LW test (Ledoit and Wolf, Ann. Stat. 30 (2002) 1081-1102) on identity tests for high dimensional data using random matrix theories. Compared with existing CLRT and LW tests, the new tests can accommodate data which has unknown means and non-Gaussian distributions. Simulations demonstrate that the new tests have good properties in terms of size and power. What is more, even for Gaussian data, our new tests perform favorably in comparison to existing tests. Finally, we find the CLRT is more sensitive to eigenvalues less than 1 while the LW test has more advantages in relation to detecting eigenvalues larger than 1.Comment: 16 pages, 2 figures, 3 tables, To be published in the Journal of Multivariate Analysi

    Optimal feature selection for sparse linear discriminant analysis and its applications in gene expression data

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    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 l1l_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.Comment: 20 pages, 3 figures, 5 tables, accepted by Computational Statistics and Data Analysi

    Limiting spectral distribution of large-dimensional sample covariance matrices generated by VARMA

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    The existence of a limiting spectral distribution (LSD) for a large-dimensional sample covariance matrix generated by the vector autoregressive moving average (VARMA) model is established. In particular, we obtain explicit forms of the LSDs for random matrices generated by a first-order vector autoregressive (VAR(1)) model and a first-order vector moving average (VMA(1)) model, as well as random coefficients for VAR(1) and VMA(1). The parameters for these explicit forms are also estimated. Finally, simulations demonstrate that the results are effective.Large-dimensional random matrices Limiting spectral distribution Vector autoregression

    Isolation and functional diversification of dihydroflavonol 4-Reductase gene HvDFR from Hosta ventricosa indicate its role in driving anthocyanin accumulation

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    Anthocyanins are natural colorants are synthesized in a branch of the flavonoid pathway. Dihydroflavonol-4reductase (DFR) catalyzes dihydroflavonoids into anthocyanins biosynthesis, which is a key regulatory enzyme of anthocyanin biosynthesis in plants. Hosta ventricosa is an ornamental plant with elegant flowers and rich colorful leaves. How the function of HvDFR contributes to the anthocyanins biosynthesis is still unknown. In this study, the DFR homolog was identified from H. ventricosa and sequence analysis showed that HvDFR possessed the conserved NADPH binding and catalytic domains. A phylogenetic analysis showed that HvDFR was close to the clade formed with MaDFR and HoDFR in Asparagaceae. Gene expression analysis revealed that HvDFR was constitutive expressed in all tissues and expressed highly in flower as well as was positively correlated with anthocyanin content. In addition, the subcellular location of HvDFR showed that is in the nucleus and cell membrane. Overexpression of HvDFR in transgenic tobacco lines enhanced the anthocyanins accumulation along with the key genes upregulated, such as F3H, F3ʹH, ANS, and UFGT. Our results indicated a functional activity of the HvDFR, which provide an insight into the regulation of anthocyanins content in H. ventricosa
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