Recursive estimation for sliced inverse regression

In this paper, we study a recursive estimation procedure for sliced inverse regression. When the number H of slices is equal to two, we obtain an analytic expression of the estimator of the direction of the parameter theta in the semiparametric regression modely = f(x' theta, epsilon), which does not require the estimation of the link function f. We propose a recursive estimation procedure for this estimator. We establish some asymptotic properties of the estimator. A simulation study illustrates the good numerical behavior of the estimator. The recursive approach has the advantage to be computationaly faster than the non recursive one.