Robustness diagnosis for bootstrap inference

Abstract

We propose a new robustness diagnostic scheme for bootstrap inference procedures. The scheme is adaptive to the data actually observed, applies readily to bootstrap inference output of diverse format, and therefore provides robustness diagnostics practically more relevant than most conventional robustness measures. Specifically, it monitors the sensitivity of the bootstrap distribution of inference output to specially designed omnidirectional data perturbations, and quantifies findings by a standardized measure with the aid of repeated resampling. The resulting measure, displayed in the form of an R-value plot, permits direct comparisons across different bootstrap procedures and across inference output of different types. Numerical examples are presented using both simulated and real-life data to illustrate applications of the scheme to estimation and hypothesis testing problems. This article has supplementary material online. © 2011 American Statistical Association.