2019
Том 71
№ 10

All Issues

Fazekas L.

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 (English)

On the rosenthal inequality for mixing fields

Fazekas L., Kukush A. G., Tómács T.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 2. - pp. 266-276

A proof of the Rosenthal inequality for α-mixing random fields is given. The statements and proofs are modifications of the corresponding results obtained by Doukhan and Utev.