From rank tests to semiparametrics

Peter Bickel
University of California, Berkeley

     Rank based tests have played a major role in
Erich Lehmann's fundamental contributions to statistics.
     In his work, much of it with J.L.Hodges Jr., he
showed how to translate rank based tests into confidence
procedures and estimates and hence into general robust
methods for linear models. A presentation at a relatively
elementary level is in his 1975 book "Nonparametrics:
Statistical methods based on ranks".
     After reviewing Lehmann's work  I will discuss how
rank based models and methods  evolved in semiparametric
models in survival analysis and econometrics and how they
are surfacing in nonparametric classification and clustering
(Machine Learning).