Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution unveiled where the number of factors could be high-dimensional. It is also shown that the new test has control over the asymptotic significance level and can be calculated efficiently. A generic method for building dependency graphs without Gaussian assumption using the new test is elaborated. Numerical results and real data analysis show the superiority of the new method.

Consider a linear model Y= X + z, where X= X n, p and z~ N (0, I n). The vector is unknown and it is of interest to separate its nonzero coordinates from the zero ones (ie, variable selection). Motivated by examples in long-memory time series (Fan and Yao, 2003) and the change-point problem (Bhattacharya, 1994), we are primarily interested in the case where the Gram matrix G= X X is non-sparse but sparsifiable by a finite order linear filter. We focus on the regime where signals are both rare and weak so that successful variable selection is very challenging but is still possible.

Improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data. Both involve estimation of the covariance function. Yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points. A class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed. A kernel estimator for estimating the nonparametric variance function is developed. Two methods for estimating parameters in the correlation structurea quasi-likelihood approach and a minimum generalized variance methodare proposed. A semiparametric varying coefficient partially linear model for longitudinal data is introduced, and an estimation procedure for model coefficients using a profile weighted least squares approach

Large-scale multiple testing with correlated and heavy-tailed data arises in a wide range of research areas from genomics, medical imaging to finance. Conventional methods for estimating the false discovery proportion (FDP) often ignore the effect of heavy-tailedness and the dependence structure among test statistics, and thus may lead to inefficient or even inconsistent estimation. Also, the commonly imposed joint normality assumption is arguably too stringent for many applications. To address these challenges, in this article we propose a factor-adjusted robust multiple testing (FarmTest) procedure for large-scale simultaneous inference with control of the FDP. We demonstrate that robust factor adjustments are extremely important in both controlling the FDP and improving the power. We identify general conditions under which the proposed method produces consistent estimate of the FDP. As a byproduct that is

Local quasi-likelihood estimation is useful for nonparametric modeling in a widely-used exponential family of distributions, called generalized linear models. Yet, the technique cannot be directly applied to situations where a response variable is missing at random. Three local quasi-likelihood estimation techniques are introduced: the local quasi-likelihood estimator using only complete-data; the locally weighted quasi-likelihood method; the local quasi-likelihood estimator with imputed values. These estimators share basically the same first order asymptotic biases and variances. Our simulation results show that substantial efficiency gains can be obtained by using the local quasi-likelihood estimator with imputed values. We develop the local quasi-likelihood imputation methods for estimating the mean functional of the response variable. It is shown that the proposed mean imputation estimators are asymptotically normal with asymptotic variance that can be easily estimated. Data from an ongoing environmental epidemiologic study is used to illustrate the proposed methods.