This package implements methods from the papers Post-selection inference: estimation of leverage and squared error optimism via flows and Degrees of freedom for piecewise Lipschitz estimators by Frederik Vissing (formerly Riis) Mikkelsen and Niels Richard Hansen.

These papers develop valid estimates of covariance penalties after model selection, which quantify leverage of individual observations as well as the total optimism of the training squared error. The resulting information criterion (YAIC) is an approximately unbiased estimate of mean squared error. This should be contrasted to AIC, Mallows's Cp and SURE that do not correctly account for model selection and are thus overly optimistic, just as classical leverage quantities underestimate the influence of individual observations when model selection is used.

YAIC is based on properties of the model selection algorithm as a function of one or more tuning parameters that allow for direct estimation of covariance penalties. Alternatives for estimating covariance penalties include bootstrapping and leave-one-out cross-validation. Compared to these methods, YAIC has a small computational overhead on top of the computation of the regularization path of estimates parametrized by the tuning parameter.

The package supports tuning parameter selection and model averaging (under development) using YAIC for Gaussian linear regression models. Extensions to generalized linear models is under development.

TODO

The package requires a model matrix and a vector of responses. Using one of the supported variable selection algorithms it returns an object with regression parameter estimates parametrized by the tuning parameter(s).