Bias correction of nonlinear orthogonal regression Istv´anFazekas ∗ Institute of Informatics, University of Debrecen P.O. B. 12, 4010 Debrecen, Hungary, fazekasi@inf.unideb.hu Alexander Kukush † Department of Mathematics and Mechanics, Kiev University Vladimirskaya st. 64, 01601, Kiev, Ukraine alexander kukush@univ.kiev.ua Silvelyn Zwanzig Department of Mathematics, Uppsala University Box 480, SE-75106, Uppsala, Sweden, 20@math.uu.se Abstract For any regression function which is nonlinear in the variables it is shown that the orthogonal regression procedure delivers an incon- sistent estimator. A new technical approach to inconsistency proof is presented, which is based on the implicit function theorem. For small measurment errors a leading term of asymptotic bias of the estimator is derived. A corrected estimator is constructed, which has smaller asymptotic bias for small measurement errors. Keywords: Asymptotic bias, Bias correction, Inconsistency, Nonlinear functional errors-in-variables models, Orthogonal distance regression. * Partially supported by the Hungarian Foundation of Scientific Researches under Grant No. OTKA T032361/2000 and Grant No. OTKA T032658/2000. † The research was partially realized while this author was visiting University of Debrecen. 1