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Motivation The functions of genes in networks are typically correlated due to their functional connectivity. Variable selection methods have been developed to select important genes associated with a trait while incorporating network graphical information. However, no method has been proposed to quantify the uncertainty of individual genes under such settings. Results In this paper, we construct confidence intervals (CIs) and provide P -values for parameters of a high-dimensional linear model incorporating graphical structures where the number of variables p diverges with the number of observations. For combining the graphical information, we propose a graph-constrained desparsified LASSO (least absolute shrinkage and selection operator) (GCDL) estimator, which reduces dramatically the influence of high correlation of predictors and enjoys the advantage of faster computation and higher accuracy compared with the desparsified LASSO. Theoretical results show that the GCDL estimator achieves asymptotic normality. The asymptotic property of the uniform convergence is established, with which an explicit expression of the uniform CI can be derived. Extensive numerical results indicate that the GCDL estimator and its (uniform) CI perform well even when predictors are highly correlated. Availability and implementation An R package implementing the proposed method is available at https://github.com/XiaoZhangryy/gcdl. [ABSTRACT FROM AUTHOR]

Trace regression has received a lot of attention due to its ability to account for matrix-type covariates, including panel data, images, and genomic microarrays as special cases. However, most of its existing research focuses on the case of mean regression. In this paper, we consider the expectile trace regression, which can provide a more diversified picture of the regression relationship at different expectiles, via the low-rank and group sparsity regularization. The upper bound for the statistical rate of convergence of the regularized estimator is established under some mild conditions. Some simulations, as well as a real data example, are also provided to illustrate the finite sample performance of the developed expectile trace regression. [ABSTRACT FROM AUTHOR]

In this paper, we study the hypothesis test for regression coefficients of partially linear models when the number of covariates in the linear part diverges. We propose a U-type test statistic. Asymptotic properties of the proposed test statistic are derived under null and local alternative on mild conditions. Extensive numerical examples are presented to demonstrate the advantages of the proposed test statistic for finite sample size. [ABSTRACT FROM AUTHOR]

In factor models, noises are often assumed to be weakly correlated; otherwise, separation of factors from noises becomes difficult, if not impossible. This paper will address this problem. We utilize an econometric idea, the so called common correlated effects (CCE) to estimate time varying factor models. We first cross sectionally average the covariates and then project the responses to the space spanned by the averaged covariates. By doing so, noises are diminished while factors are distinguished. The advantages of our new estimators are two folds. First, the convergence rates of estimated factors and loadings are independent of cross sectional dimension. Second, our new estimators are robust to the correlation of noises. Hence our new estimators can, on one hand, separate market factors for the stock data set used in this paper even if noises exhibit strong correlations within industries due to industry-specific factors and on the other hand, avoid inappropriately absorbing industry-specific factors into market factors. [ABSTRACT FROM AUTHOR]

This paper investigates the series correlation test for the partially functional linear regression model (PFLRM). PFLRM relates a scalar response to the predictor variable that is composed of multivariate vectors and random functions. We propose two test statistics for series correlation in PFLRM and derive their asymptotic distributions under the null hypothesis. Numerical studies with finite sample size reveal that the proposed statistics have good performances. Finally, we explore the application of the tests on the electricity consumption data which shows that our test statistics are effective and stable. [ABSTRACT FROM AUTHOR]

This article investigates the testing for serial correlation in partially linear models with validation data and applies the empirical likelihood methods to construct serial tests statistics, and then we derive the asymptotic distribution of the test statistics under null hypothesis. Simulation results show that our method performs well. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the testing for serial correlation in a linear model with validation data, then we apply the empirical likelihood method to construct the test statistic and derive the asymptotic distribution of the test statistic under null hypothesis. Simulation results show that our method performs well both in size and power with finite same size. [ABSTRACT FROM AUTHOR]