A sign and rank based semiparametrically efficient estimator for regression analysis

In regression analysis it is well known that skewness and excessive tail heaviness affect the efficiency of classical estimators. In this work, we propose an estimator that is highly efficient for a wide range of distributions. More specifically, in accordance with standard Le Cam theory, we define a sign and rank based estimator of the regression coefficients as a one-step update, based on a fully semiparametrically efficient central sequence, of an initial root n consistent estimator. In the central sequence, the score function, initially defined on the basis of the exact underlying innovation density f, is estimated using the fact that f can be well adjusted by a Tukey g-and-h distribution. We present the results of some Monte Carlo simulations conducted to assess the finite sample performance of our estimator, in comparison with the ordinary least squares estimator and the approximated maximum likelihood estimator. We propose a Stata command flexrank to implement it in practice. The procedure is very fast and has a low computational complexity.