Testing covariates in high dimension linear regression with latent factors

Testing covariates in high-dimensional regression

Abstract In a high-dimensional linear regressionmodel, we propose a new procedure for testing statistical significance of a subset of regression coefficients. Specifically, we employ the partial covariances between the response variable and the tested covariates to obtain a test statistic. The resulting test is applicable even if the predictor dimension is much larger than the sample size. Unde...

Non linear robust regression in high dimension

Semiparametric Quantile Regression with High-dimensional Covariates.

This paper is concerned with quantile regression for a semiparametric regression model, in which both the conditional mean and conditional variance function of the response given the covariates admit a single-index structure. This semiparametric regression model enables us to reduce the dimension of the covariates and simultaneously retains the flexibility of nonparametric regression. Under mil...

Multiple testing in high-dimensional linear regression

In many real-world statistical problems, we observe a large number of potentially explanatory variables of which a majority may be irrelevant. For this type of problem, controlling the false discovery rate (FDR) guarantees that most of the discoveries are truly explanatory and thus replicable. In this talk, we propose a new method named SLOPE to control the FDR in sparse high-dimensional linear...

Testing Endogeneity with High Dimensional Covariates∗

Modern, high dimensional data has renewed investigation on instrumental variables (IV) analysis, primary focusing on estimation of the included endogenous variable under sparsity and little attention towards specification tests. This paper studies in high dimensions the Durbin-Wu-Hausman (DWH) test, a popular specification test for endogeneity in IV regression. We show, surprisingly, that the D...