Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others. While a large variety of results provide tight bounds on the average errors between empirical and population statistics of eigenvectors, fewer results are tight for entrywise analyses, which are critical for a number of problems such as community detection and ranking.

We propose a novel technique to boost the power of testing a highdimensional vector <i>H</i>:<i><b></b></i>=<b>0</b> against sparse alternatives where the null hypothesis is violated by only a few components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due to the accumulation of errors in estimating highdimensional parameters. More powerful tests for sparse alternatives such as thresholding and extreme value tests, on the other hand, require either stringent conditions or bootstrap to derive the null distribution and often suffer from size distortions due to the slow convergence. Based on a screening technique, we introduce a power enhancement component, which is zero under the null hypothesis with high probability, but diverges quickly under sparse alternatives. The proposed test statistic combines the power enhancement component with an asymptotically pivotal statistic, and

Severe acute respiratory syndrome (SARS) is a new infectious disease with a global impact. Understanding its pathogenesis and developing specific diagnostic methods for its early diagnosis are crucial for the effective management and control of this disease. By using proteomic technology, truncated forms of ₁antitrypsin (TF₁AT) were found to increase significantly and consistently in sera of SARS patients compared to control subjects. The result showed a sensitivity of 100% for SARS patients and a specificity of 92.8% for controls. Furthermore, the levels of these proteins significantly correlated with certain clinicopathological parameters. The dramatic increase in TF₁AT may be the result of degradation of ₁AT. As ₁AT plays an important role in the protection of lung function, its degradation may be an important factor in the pathogenesis of SARS. These findings indicate that increased TF₁AT

<b></b> Estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits. We present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points. Specifically, we adopt Huang et al.'s (2006,<i>Biometrika</i><b>93</b>, 8598) approach of invoking the modified Cholesky decomposition and converting the problem into modeling a sequence of regressions of responses. A regularized covariance estimator is obtained using a normal penalized likelihood with an<i>L</i>₂ penalty. This approach, embedded within a mixture likelihood framework, leads to enhanced accuracy, precision, and flexibility of functional mapping while preserving its biological relevance. Simulation studies are

This paper discusses statistical methods for estimating complex correlation structure from large pharmacogenomic datasets. We selectively review several prominent statistical methods for estimating large covariance matrix for understanding correlation structure, inverse covariance matrix for network modeling, large-scale simultaneous tests for selecting significantly differently expressed genes and proteins and genetic markers for complex diseases, and high dimensional variable selection for identifying important molecules for understanding molecule mechanisms in pharmacogenomics. Their applications to gene network estimation and biomarker selection are used to illustrate the methodological power. Several new challenges of Big data analysis, including complex data distribution, missing data, measurement error, spurious correlation, endogeneity, and the need for robust statistical methods, are also discussed.