Colloquium

Department of Statistics

Conference on Robust Rank-Based and Nonparametric Methods
April 9 (Fri) 5 p.m.

Rank Based Analysis of Linear Models and Beyond: a review

Tom Hettmansperger
Penn State University

In the 1940s Wilcoxon, Mann and Whitney, and others began the development of rank based methods for basic one and two sample models. Over the years a multitude of papers have been written extending the use of ranks to more and more complex models. In the late 60s and early 70s Jureckova and Jaeckel along with others provided the necessary asymptotic machinery to develop rank based estimates in the linear model.

Beginning with his 1975 thesis, Joe McKean has worked with many students and coauthors to develop a unified approach to data analysis (model fitting, inference, diagnostics, and computing) based on ranks. This approach includes the linear model and various extensions, for example multivariate models and models with dependent error structure such as mixed models, time series models, and longitudinal data models. Moreover, McKean and Kloke have developed an R library to implement this methodology.

This talk will review the development of this methodology with particular emphasis on the work of Joe McKean. Along the way we will illustrate the surprising ubiquity of ranks throughout statistics.