Largescale multiple testing with correlated test statistics arises frequently in much scientific research. Incorporating correlation information in approximating the false discovery proportion (FDP) has attracted increasing attention in recent years. When the covariance matrix of test statistics is known, Fan and his colleagues provided an accurate approximation of the FDP under arbitrary dependence structure and some sparsity assumption. However, the covariance matrix is often unknown in many applications and such dependence information must be estimated before approximating the FDP. The estimation accuracy can greatly affect the FDP approximation. In the current paper, we study theoretically the effect of unknown dependence on the testing procedure and establish a general framework such that the FDP can be well approximated. The effects of unknown dependence on approximating the FDP are in the

We have collected and cleaned two network data sets: Coauthorship and Citation networks for statisticians. The data sets are based on all research papers published in four of the top journals in statistics from 2003 to the first half of 2003 . We analyze the data sets from many different perspectives, focusing on (a) productivity, patterns and trends,(b) centrality and (c) community structures.

Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression models is a regression parameter function in one or two arguments. If, in addition, one has scalar predictors, as is often the case in applications to longitudinal studies, the question arises how to incorporate these into a functional regression model. We study a varying-coefficient approach where the scalar covariates are modeled as additional arguments of the regression parameter function. This extension of the functional linear regression model is analogous to the extension of conventional linear regression models to varying-coefficient models and shares its advantages, such as increased flexibility; however, the details of this extension are more challenging in the functional case. Our

In the analysis of cluster data the regression coefficients are frequently assumed to be the same across all clusters. This hampers the ability to study the varying impacts of factors on each cluster. In this paper, a semiparametric model is introduced to account for varying impacts of factors over clusters by using cluster-level covariates. It achieves the parsimony of parametrization and allows the explorations of nonlinear interactions. The random effect in the semiparametric model accounts also for within cluster correlation. Local linear based estimation procedure is proposed for estimating functional coefficients, residual variance, and within cluster correlation matrix. The asymptotic properties of the proposed estimators are established and the method for constructing simultaneous confidence bands are proposed and studied. In addition, relevant hypothesis testing problems are addressed. Simulation studies are

This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest \mathbf {x}^{atural}\in\mathbb {R}^{n} from \mathbf {x}^{atural}\in\mathbb {R}^{n} quadratic equations/samples \mathbf {x}^{atural}\in\mathbb {R}^{n} , \mathbf {x}^{atural}\in\mathbb {R}^{n} . This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning.