The problem of approximating a general regression function m(x) = E (Y IX = x) is addressed. As in the case of the c1assical L2-type projection pursuit regression considered by Hall (1989), we propose to approximate m(x) through a regression of Y given an index, that is a unidimensional...

Semiparametric single-index regression involves an unknown finite dimensional parameter and an unknown (link) function. We consider estimation of the parameter via the pseudo maximum likelihood method. For this purpose we estimate the conditional density of the response given a candidate index...