Efron holds his belief

The Efron dice voting system

About …fty years ago, Efron noted some counterintuitive properties of the long-term behavior of contests involving dice. For instance, consider the 6-sided dice whose sides are labeled (4,4,4,4,0,0), (3,3,3,3,3,3), (6,6,2,2,2,2), and (5,5,5,1,1,1). Each die has a 2/3 probability of rolling a higher number than the next one in the list, and the last has the same 2/3 probability of rolling a high...

Discussion of “ Least Angle Regression ” by Efron

Algorithms for simultaneous shrinkage and selection in regression and classification provide attractive solutions to knotty old statistical challenges. Nevertheless, as far as we can tell, Tibshirani’s Lasso algorithm has had little impact on statistical practice. Two particular reasons for this may be the relative inefficiency of the original Lasso algorithm and the relative complexity of more...

Discussion of “ Least Angle Regression ” by Efron

I would like to begin by congratulating the authors (referred to below as EHJT) for their interesting paper in which they propose a new variable selection method (LARS) for building linear models and show how their new method relates to other methods that have been proposed recently. I found the paper to be very stimulating and found the additional insight that it provides about the Lasso techn...

Efron–stein Inequalities for Random Matrices By

Discussion of “ Least Angle Regression ” by Efron

Most of this article concerns the uses of LARS and the two related methods in the age-old, " somewhat notorious, " problem of " [a]utomatic model-building algorithms.. . " for linear regression. In the following, I will confine my comments to this notorious problem and to the use of LARS and its relatives to solve it. 1. The implicit assumption. Suppose the response is y, and we collect the m p...