Том 71
№ 6

All Issues

Zwanzig S.

Articles: 2
Article (English)

Correction of nonlinear orthogonal regression estimator

Fazekas L., Kukush A. G., Zwanzig S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1101–1118

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.

Article (Russian)

On an Adaptive Estimator of the Least Contrast in a Model with Nonlinear Functional Relations

Kukush A. G., Zwanzig S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 9. - pp. 1204-1209

We consider an implicit nonlinear functional model with errors in variables. On the basis of the concept of deconvolution, we propose a new adaptive estimator of the least contrast of the regression parameter. We formulate sufficient conditions for the consistency of this estimator. We consider several examples within the framework of the L 1- and L 2-approaches.