**Kjell Doksum **

University of Wisconsin

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.