## AlgorithmWe consider linear regression model, where we are given i.i.d. pairs , , , with vectors and response variables are given by
In matrix form, letting and denoting by the design matrix with rows , we have
Goal
Given response vector and design matrix , we want to construct confidence intervals for each single coefficient .
Here, we provide a simple explanation of our method. For more details and discussions, please see our paper. Our method is based on constructing a ‘de-biased’ version of LASSO. Let be the LASSO estimator with regularization parameter . For a matrix , define
For and significance , we let
For testing the null hypothesis , we construct a two-sided -value as follows:
For input parameter , the de-biasing matrix is constructed via the following optimization problem: 1. Let be a solution of the convex program:
2. Set ( Rows of are the vectors .) In our code, the user can either give parameters and as input or let the algorithm select their values automatically. |