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@article{SJIM_2016_19_4_a5, author = {A. A. Lomov}, title = {On the asymptotic optimality of orthoregressional estimates}, journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki}, pages = {51--60}, publisher = {mathdoc}, volume = {19}, number = {4}, year = {2016}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SJIM_2016_19_4_a5/} }
A. A. Lomov. On the asymptotic optimality of orthoregressional estimates. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 4, pp. 51-60. http://geodesic.mathdoc.fr/item/SJIM_2016_19_4_a5/
[1] Adcock R. J., “Note on the method of least squares”, The Analyst, 4 (1877), 183–184 | DOI
[2] Adcock R. J., “A problem in least squares”, The Analyst., 5 (1878), 53–54 | DOI
[3] Kummel C. H., “Reduction of observed equations which contain more then one observed quantity”, The Analyst., 6 (1879), 97–105 | DOI
[4] Pearson K., “On lines and planes of closest fit to systems of points in space”, Philosophical Magazine, 6:2 (1901), 559–572 | DOI | Zbl
[5] Gauss K. F., Izbrannye geodezicheskie sochineniya, v. 1, Geodezizdat, M., 1957, 59–87
[6] Kramer G., Matematicheskie metody statistiki, Nauka, M., 1975 | MR
[7] Golub G. H., Van Loan C. F., “An analysis of the total least squares problem”, SIAM J. Numer. Anal., 17 (1980), 883–893 | DOI | MR | Zbl
[8] Koopmans T. C., Linear Regression Analysis of Economic Time Series, Haarlem, 1937
[9] Levin M. J., “Estimation of a system pulse transfer function in the presence of noise”, IEEE Trans. Automat Control, AC-9 (1964), 229–235 | DOI
[10] Markovsky I., Van Huffel S., “Overview of total least squares methods”, Signal Processing, 87 (2007), 2283–2302 | DOI | Zbl
[11] Egorshin A. O., “Vychislitelnye zamknutye metody identifikatsii lineinykh ob'ektov”, Optimalnye i samonastraivayuschiesya sistemy, Novosibirsk, 1971, 40–53
[12] Egorshin A. O., “Metod naimenshikh kvadratov i “bystrye”algoritmy v variatsionnykh zadachakh identifikatsii i filtratsii (metod VI)”, Avtometriya, 1988, no. 1, 30–42
[13] Moor De B., “Structured total least squares and $L_2$ approximation problems”, Linear Algebra Appl., 188–189 (1993), 163–207 | DOI | MR
[14] Lomov A. A., “Variatsionnye metody identifikatsii lineinykh dinamicheskikh sistem i problema lokalnykh ekstremumov”, Upravlenie bolshimi sistemami, 39, 2012, 53–94 URL: http://ubs.mtas.ru/upload/library/UBS3903.pdf
[15] Lomov A. A., “O sostoyatelnosti obobschennykh ortoregressionnykh otsenok parametrov lineinoi dinamicheskoi sistemy”, Cib. zhurn. industr. matematiki, 16:4(56) (2013), 87–93 | MR | Zbl
[16] Kahn M., Mackisack M. S., Osborne M. R., Smyth G. K., “On the consistency of Prony's method and related algorithms”, J. Comput. Graph. Statist., 1 (1992), 329–349 | MR
[17] Heij C., Scherrer W., “Consistency of system identification by global total least squares”, Automatica, 35 (1999), 993–1008 | DOI | MR | Zbl
[18] Kukush A., Markovsky I., Van Huffel S., “Consistency of the structured total least squares estimator in a multivariate errors-in-variables model”, J. Statist. Plann. Inference, 133:2 (2005), 315–358 | DOI | MR | Zbl
[19] 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
[20] Fuller W. A., Measurement Error Models, Wiley, N.Y., 1987 | MR | Zbl
[21] Lomov A. A., “Ortoregressionnye otsenki parametrov sistem lineinykh raznostnykh uravnenii”, Sib. zhurn. industr. matematiki, 8:3(23) (2005), 102–119 | MR | Zbl
[22] Lomov A. A., “Identifikatsiya lineinykh dinamicheskikh sistem po korotkim uchastkam perekhodnykh protsessov pri additivnykh izmeritelnykh vozmuscheniyakh”, Izvestiya RAN. TSU, 1997, no. 3, 20–26 | Zbl
[23] Lomov A. A., “Usloviya razlichimosti statsionarnykh lineinykh sistem”, Differents. uravneniya, 39:2 (2003), 261–266 | MR | Zbl
[24] 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
[25] Lemmerling Ph., Mastronardi N., Van Huffel S., “Fast algorithm for solving the Hankel/Toeplitz structured total least squares problem”, Numer. Algorithms, 23 (2000), 371–392 | DOI | MR | Zbl
[26] Borovkov A. A., Matematicheskaya statistika, Nauka, Izd-vo In-ta matematiki, Novosibirsk, 1997 | MR
[27] Li R., Optimalnye otsenki, opredelenie kharakteristik i upravlenie, Nauka, M., 1966