This IMA Volume in Mathematics and its Applications DIRECTIONS IN ROBUST STATISTICS AND DIAGNOSTICS is based on the proceedings of the first four weeks of the six week IMA 1989 summer program "Robustness, Diagnostics, Computing and Graphics in Statistics". An important objective of the organizers was to draw a broad set of statisticians working in robustness or diagnostics into collaboration on the challenging problems in these areas, particularly on the interface between them. We thank the organizers of the robustness and diagnostics program Noel Cressie, Thomas P. Hettmansperger, Peter J. Huber, R. Douglas Martin, and especially Werner Stahel and Sanford Weisberg who edited the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Central themes of all statistics are estimation, prediction, and making decisions under uncertainty. A standard approach to these goals is through parametric mod­ elling. Parametric models can give a problem sufficient structure to allow standard, well understood paradigms to be applied to make the required inferences. If, how­ ever, the parametric model is not completely correct, then the standard inferential methods may not give reasonable answers. In the last quarter century, particularly with the advent of readily available computing, more attention has been paid to the problem of inference when the parametric model used is not correctly specified.

Content.- Small sample properties of robust analyses of linear models based on R-estimates: A survey.- Regression diagnostics for rank-based methods II.- Robust multivariate spectral analysis of the EEG.- Configural polysampling.- Robustness to unequal scale and other departures from the classical linear model.- Unmasking multivariate outliers and leverage points by means of BMDP3R.- Glimpse: An assessor of GLM misspecification.- Regression quantile diagnostics for multiple outliers.- Robust testing of functionals.- Robustness of the p-subset algorithm for regression with high breakdown point.- Robust distances: Simulations and cutoff values.- Diagnostics for regression-ARMA time series.- General approaches to stepwise identification of unusual values in data analysis.- Research directions in robust statistics.- Comparisons between first order and second order approximations in regression diagnostics.- Consumer datesware.- Graphical displays for alternate regression fits.- Some issues in the robust estimation of multivariate location and scatter.- Adaptive efficient weighted least squares with dependent observations.- A procedure for robust estimation and inference in linear regression.- Author index.