72 – Miscellaneous Computational Methods
User-Oriented High-Dimensional Linear Model Estimation
Taylor Arnold
Yale University
Penalized M-estimators have garnered much attention in recent years for their use in estimating regression parameters in high dimensional linear models. A large amount of work as been done to produce ef�cient algorithms and code for solving the underlying optimization problems of these methods and extending results to related applied topics (e.g., graphical models, generalized linear models). Unfortunately, these optimization schemes have not been paired with recent theoretical innovations in order provide maximum utility to practitioners. Current R packages, for instance, tune models with inconsistent cross validation procedures rather than easy to compute choices based on analytical properties of the penalized estimator. The package hdlm recti�es this gap by using tuning parameters which guarantee asymptotic consistency as well calculating valid p values, standard errors, ANOVA tables, and producing useful graphical outputs. We pay particular attention to computational speed and memory issues which arise as a result of the resampling required to produce empirical p values and standard errors.
