Abstract
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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 8, pp. 1101–1118, August, 2004.
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Fazekas, I., Kukush, A. & Zwanzig, S. Correction of nonlinear orthogonal regression estimator. Ukr Math J 56, 1308–1330 (2004). https://doi.org/10.1007/s11253-005-0059-0
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DOI: https://doi.org/10.1007/s11253-005-0059-0