Double bootstrap for shrinkage estimators

Computer-intensive bootstrap methods are potentially problematic when applied to biased estimators similar to ridge regression, because biased estimators may lack a pivot. We propose a modification for Efronʹs bias corrected percentiles and suggest an approximate pivoting transformation for ridge regression. We indicate practical aspects of Beranʹs double bootstrap designed specifically for situations where there is nonnormality and a lack of a pivot. Econometric applications to estimating consumption functions, a simulation with multicollinear data and new graphical tools are included.