Correction of nonlinear orthogonal regression estimator - Fazekas, L.; Kukush, A. G.; Zwanzig, S. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
For any nonlinear regression function, it is shown that the orthogonal regression procedure delivers an inconsistent estimator. A new technical approach to the proof of inconsistency based on the implicit-function theorem is presented. For small measurement errors, the leading term of the asymptotic expansion of the estimator is derived. We construct a corrected estimator, which has a smaller asymptotic deviation for small measurement errors.