On a corrected contrast estimator in the implicit nonlinear functional relation model Alexander Kukush University of Kiev Silvelyn Zwanzig University of Hamburg October 1997 Preprint 97-11 Institute for Mathematical Stochastics University of Hamburg Bundesstr.55 D-20146 Hamburg, Germany Abstract For the implicit nonlinear functional relation model a new cor- rected contrast estimation procedure is proposed, which is based on the deconvolution idea and eliminates the nuisance parameters in the usual minimum contrast function. The sufficient conditions for con- sistency are given. Several examples are considered including L 1 and L 2 methods. Contents 1 Introduction The aim of this paper is to present a new corrected minimum contrast func- tion in the implicit functional relation model. The functional relation model is characterized by an increasing number of nuisance parameters and a fixed number of parameters of interest. It is an old fact that in models with an increasing number of nuisance parameters 1