A note on the statistical properties of the secant algorithm for calculating rank estimators

We examine the statistical properties of the result of a single step of the secant algorithm for calculating rank based or R-estimators. In particular, we show that for problems involving a single parameter, the result of a single step of the secant algorithm is asymptotically equivalent (in a statistical sense) to the R-estimator and, that for regression problems with more than one parameter, one step of the secant algorithm provides an appropriate estimate of the magnitude of the next step in the usual one-step algorithm.