Confidence intervals using the graphical Lasso

Speaker(s): 
Sara van de Geer (ETH Zürich)
Date: 
Wednesday, July 2, 2014 - 10:00am
Location: 
Mohrenstraße 39, Erhard-Schmidt-Hörsaal

Over the recent years much statistical theory and methodology for high-dimensional problems has been developed. However, the question of statistical inference in the sense of testing and confidence intervals is less well addressed. In this talk, we consider data consisting of i.i.d. copies a high-dimensional vector X. The aim is to estimate the precision matrix (the inverse of the covariance matrix of X). We use the graphical Lasso as initial estimator and then ”de-sparsify” it. Under certain (sparsity) conditions the entries of this new estimator are asymptotically normal. This leads to the construction of asymptotic confidence intervals. We illustrate the theory with a simulation study. We also discuss the extension to other l1-penalized M-estimators and the concept of worst possible sub-directions.

Joint work with Jana Jankova.