B1960
Title: Least angle regression inference
Authors: Karl Gregory - University of South Carolina (United States) [presenting]
Daniel Nordman - Iowa State University (United States)
Abstract: The aim is to make inferences on parameters derived from the population path of the least-angle regression algorithm. Least angle regression was introduced as a data-based algorithm which admits predictor variables sequentially into a linear regression model; we formulate its population path as a function of the true linear regression coefficients, conditioning on the empirical covariance matrix of the predictor variables. For each predictor, we treat as the object of our inference its correlation with the current residual upon its entrance into the path. We find that we can construct reliable individual and simultaneous confidence intervals for these quantities using the bootstrap. We consider the supposition that nonzero entrance correlations indicate variable importance in the model; when this supposition is correct, we may infer the importance of a predictor when the confidence interval for its entrance correlation excludes zero, providing an alternative to classical regression inference. We ask in what settings nonzero entrance correlations truly imply variable importance and study the robustness of our inferences when these settings do not hold.
