Geodesic
Orthoregressive estimates for the parameters of systems of linear difference equations
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 3, pp. 102-119.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of estimating the parameters of linear difference systems of equations from the observations of the segments of solutions with additive stochastic perturbations is considered. The methods of multivariate orthogonal regression are applied to obtain the estimators. The results of comparative study of the methods are exposed from the standpoint of information on linear constraints in observations. The properties of the estimators in the limit cases of a gross sample are studied. For small perturbations, a scheme for comparison of estimators by linear approximations is proposed. 
@article{SJIM_2005_8_3_a11,
     author = {A. A. Lomov},
     title = {Orthoregressive estimates for the parameters of systems of linear difference equations},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {102--119},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a11/}
}
TY  - JOUR
AU  - A. A. Lomov
TI  - Orthoregressive estimates for the parameters of systems of linear difference equations
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2005
SP  - 102
EP  - 119
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a11/
LA  - ru
ID  - SJIM_2005_8_3_a11
ER  - 
%0 Journal Article
%A A. A. Lomov
%T Orthoregressive estimates for the parameters of systems of linear difference equations
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2005
%P 102-119
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a11/
%G ru
%F SJIM_2005_8_3_a11
A. A. Lomov. Orthoregressive estimates for the parameters of systems of linear difference equations. Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 3, pp. 102-119. http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a11/

[1] Lomov A. A., “O razlichimosti statsionarnykh lineinykh sistem s koeffitsientami, zavisyaschimi ot parametra”, Sib. zhurn. industr. matematiki, 6:4(16) (2003), 60–66 | MR | Zbl

[2] Fuller W. A., Measurement Error Models, Wiley, N. Y., 1987 | MR

[3] Pearson K., “On lines and planes of closest fit to systems of points in space”, Phil. Mag., 6:2 (1901), 559

[4] Kramer G., Matematicheskie metody statistiki, Nauka, M., 1975 | MR

[5] Measurement Errors in Surveys, Wiley, N. Y., 2004

[6] Lomov A. A., “Ortoregressionnye metody otsenivaniya parametrov i zadachi otdeleniya trendov v lineinykh sistemakh”, Differentsialnye uravneniya i protsessy upravleniya, 2005, no. 2, 1–86 ; http://www.neva.ru/journal | MR | DOI

[7] Lomov A. A., “Sravnenie metodov otsenivaniya parametrov lineinykh dinamicheskikh sistem po izmereniyam korotkikh uchastkov perekhodnykh protsessov”, Avtomatika i telemekhanika, 2005, no. 3, 39–47 | MR | Zbl

[8] Lomov A. A., “O statisticheskikh svoistvakh otsenok parametrov lineinykh dinamicheskikh sistem po izmereniyam korotkikh uchastkov perekhodnykh protsessov”, Tr. 3 Mezhdunar. konf. “Identifikatsiya sistem i zadachi upravleniya SICPRO'04” (M., 28–30 yanvarya 2004), In-t problem upravleniya RAN, M., 209–224

[9] Lomov A. A., “Usloviya razlichimosti statsionarnykh lineinykh sistem”, Differents. uravneniya, 39:2 (2003), 261–266 | MR | Zbl

[10] Lomov A. A., “Identifikatsiya lineinykh dinamicheskikh sistem po korotkim uchastkam perekhodnykh protsessov pri additivnykh izmeritelnykh vozmuscheniyakh”, Izv. RAN. Teoriya i sistemy upravleniya, 1997, no. 3, 20–26 | Zbl

[11] Egorshin A. O., “Metod naimenshikh kvadratov i “bystrye” algoritmy v variatsionnykh zadachakh identifikatsii i filtratsii (metod VI)”, Avtometriya, 1988, no. 1, 30–42

[12] Aoki M., Vvedenie v metody optimizatsii, Nauka, M., 1977

[13] Aoki M., Yue P. C., “On a priori error estimates of some identification methods”, IEEE Trans. Automat. Control, AC-15 (1970), 541–548 | DOI | MR

[14] Aoki M., Yue P. C., “On the certain convergence questions in system identification”, SIAM J. Control, 8:2 (1970), 239–256 | DOI | MR | Zbl

[15] Gleser L. J., “Estimation in a multivariate “errors in variables” regression model: large sample results”, Ann. Statist., 9:1 (1981), 24–44 | DOI | MR | Zbl

[16] Borovkov A. A., Matematicheskaya statistika, Nauka, M., 1984

[17] Kostin V. I., “O tochkakh ekstremuma odnoi funktsii”, Upravlyaemye sistemy, 1984, no. 24, 35–42 | MR

[18] Lomov A. A., “Minimalnye opisaniya statsionarnykh lineinykh modelei”, Modeli i metody optimizatsii, Tr. In-ta matematiki SO RAN, 28, 1994, 91–117 | MR | Zbl

[19] Kalman R. E., “Mathematical description of linear dynamical systems”, SIAM J. Control. Ser. A, 1:2 (1963), 152–192 | DOI | MR | Zbl

[20] Leman E., Teoriya tochechnogo otsenivaniya, Nauka, M., 1991 | MR

[21] Gantmakher F. R., Teoriya matrits, Nauka, M., 1988 | MR | Zbl