Correction of nonlinear orthogonal regression estimator
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.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 8, pp 1308-1330.
Citation Example: Fazekas L., Kukush A. G., Zwanzig S. Correction of nonlinear orthogonal regression estimator // Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1101–1118.