Approximate standard errors in semiparametric models

We consider semiparametric models with p regressor terms and q smooth terms . We obtain an explicit expression for the estimate of the regression coeff icients given by the back-fitting algorithm. The calculation of the standar d errors of these estimates based on this expression is a considerable comp utational exercise. We present an alternative, approximate method of calcul ation that is less demanding. With smoothing splines, the method is exact, while with loess, it gives good estimates of standard errors. We assess the adequacy of our approximation and of another approximation with the help o f two examples.