FELLOW’S CORNER Foundations of statistical inference based on numerical roots of robust pivot functions

Fisher’s pivot functions (PFs) continue to dominate statistical inference and bootstrap literature, despite Efron and Hinkley and Royall’s attempts to inject robustness. Vinod uses Godambe’s pivot functions (GPFs) based on Godambe–Durbin estimating functions (EFs) to develop numerically computed GPF roots. Such GPF roots can fill a long-standing need in the bootstrap literature for robust pivots. Proposition 1 proves that GPFs are more robust than other PFs. Recently, Heyde rigorously explains why confidence intervals (CIs) from GPFs are the shortest and Davison and Hinkley explain why the double bootstrap (d-boot) yields second-order correct CIs. We briefly discuss realistic econometric simulations supporting GPF roots in double bootstraps.