The problem of estimating regression parameters in the usual linear model is considered when it is a prior suspected that the parameters may be restricted to a subspace and the error terms are not necessarily normally distributed. In this article, we develop the asymptotic properties of a positive part shrinkage R-estimator (PPSRE), Improved preliminary test R-estimator (IPTRE) and shrinkage preliminary test R-estimator (SPIRE) of the regression coefficients in the light of a quadratic loss function. It is shown that the proposed PPSRE and IPTRE asymptotically dominate the usual shrinkage R-estimator (SRE) and the standard preliminary test R-estimator (PTRE) respectively in a setting of local alternatives. It is also demonstrated analytically and numerically that the proposed shrinkage preliminary test R-estimator provides a wider range than the PTRE in which it dominates the unrestricted R-estimator (URE). An optimal rule for the size of the preliminary test is presented. It is found that the size of the preliminary test for the proposed SPIRE is more reasonable than the usual PTRE.