Minimum risk equivariant estimator in linear 2 regression model

The minimum risk equivariant estimator (MRE) of the regression parameter vector β 6 in the linear regression model enjoys the finite-sample optimality property, but its calculation is 7 difficult, with an exception of few special cases. We study some possible approximations of MRE, 8 with distribution of the errors being known or unknown: A finite-sample approximation uses the 9 Hájek–Hoeffding projection or the Hoeffding–van Zwet decomposition of an initial equivariant es10 timator of β, a large-sample approximation is based on the asymptotic representation of the same. 11 A nonparametric approximation uses the expected value with respect to the conditional empirical 12 distribution function, developed by Stute (1986). The only possible approximation avoiding a dif13 ficult calculation of conditional expectations is the asymptotic approximation, based on the score 14 function of the underlying distribution of the errors. 15