Non-parametric analysis of a generalized regression model: The maximum rank correlation estimator

Abstract

The paper considers estimation of a model y i = D · F( x′ i β 0, u i ), where the composite transformation D · F is only specified that D: R → R is non-degenerate monotonic and F: R 2 → R is strictly monotonic in each of its variables. The paper thus generalizes standard data analysis which assumes that the functional form of D · F is known and additive. The estimator which it proposes is the maximum rank correlation estimator which is non-parametric in the functional form of D · F and non-parametric in the distribution of the error terms, u i . The estimator is shown to be strongly consistent for the parameters β 0 up to a scale coefficient.