|
Abstract:
|
Traditional R-estimators, defined via the minimization of rank-based objective functions, are unsatisfactory not only from a practical point of view (the implementation is numerically infeasible for high-dimensional parameters), but also from a theoretical point of view (root-n consistency is nontrivial). We suggest a rank-based adaptation of Le Cam's one-step construction of locally asymptotically optimal estimators. The new estimators are asymptotically equivalent to a random vector measurable with respect to the ranks associated with the true value of the parameter, and hence can be considered as genuine R-estimators. They are easy to compute and exhibit good finite sample properties. As expected, they are locally and asymptotically optimal under correctly specified densities. Finally, their Gaussian-score versions often uniformly dominate their parametric Gaussian counterparts.
|
