Non-parametric analysis of a generalized regression model. The maximum rank correlation estimator (Q1099547)

A method of estimation for the regression model \(y_ i=D\circ F(x'_ i,\beta_ 0,u_ i)\), \(i=1,...,N\), is developed under the assumptions that the transformation \(D\circ F\) is non-degenerate and monotone and F is strictly monotone in each variable. The parameter \(\beta_ 0\) is estimated using the maximum rank correlation estimator. The method is non-parametric for the errors, which are assumed i.i.d. and in the shape of the transformation \(D\circ F\). In section 3, the consistency of the estimator up to a scale factor is proved using the SLLN for the statistics. It is also shown that the method can be applied to several models considered elsewhere in the literature. Finally, in section 4 open problems and possible generalizations are considered.