Confidence Intervals and Hypothesis Testing for High-Dimensional Regression

Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the parameter estimates. This in turn implies that it is extremely challenging to quantify the \emph{uncertainty} associated with a certain parameter estimate. Concretely, no commonly accepted procedure exists for computing classical measures of uncertainty and statistical significance as confidence intervals or $p$-values for these models. We consider here high-dimensional linear regression problem, and propose an efficient algorithm for constructing confidence intervals and…