RESUMEN
MOTIVATION: Genes function 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 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 (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 confidence interval can be derived. Extensive numerical results indicate that the GCDL estimator and its (uniform) confidence interval performs 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. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
RESUMEN
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.