Extending a Large Dimensional Empirical Likelihood Test to Regression

Using empirical likelihood methods for inference on a population mean when working with a high dimensional vector (where the dimension p is greater than the sample size n) has generally faced difficulties both because the convex hull of the observations becomes too small to cover the true mean value and because the sample covariance matrix is singular. Recent research has proposed a new strategy that addresses these two issues. An extension of this strategy towards hypothesis testing in various regression settings (linear, logistic, Poisson) is presented, with simulated data used to illustrate the test's power performance.