Sara van de Geer - The Debiased Lasso

In the third lecture we use sparsity to establish confidence intervals for a parameter of interest. The idea is to use the penalized estimator as an initial estimator in a one-step Newton-Raphson procedure. Functionals of this new estimator that can under certain conditions be shown to be asymptotically normally distributed. We show that in the high-dimensional case, one may further profit from sparsity conditions if the inverse Hessian of the problem is not sparse.