Kjell Doksum
University of Wisconsin
History of Lehmann Inference,
Plus Large Scale Covariance Estimation
Hodges and Lehmann proposed using rank test statistics evaluated at transformed data to construct estimating equations.
In the context of a model of the form Y=h(e;Z,beta), where e is a random error, this approach
corresponds to computing the the inverse e=g(Z,Y;beta) by solving Y=h(e;Z,beta) for e and using the distribution of the ranks
of independent e's as a likelihood. The properties of the resulting estimators have been developed in many important contexts.
This talk will review and extend asymptotic and semi-parametric optimality properties. Comparisons with other estimators will be presented.