Geodesic
Robust estimation of nonlinear structural models
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 47-60.

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The problem of the identification of nonlinear errors-in-variables models with large observational errors in the explanatory variable is considered. On the basis of robust estimation methods, we propose a development of the algorithms of adjusted and total least squares is suggested. This enabled us to get a better precision of the reconstruction of the response in the presence of outliers in the sample. The proposed algorithms are used in constructing the Engel curve from the data of a budget survey. As a result we managed to make more correct conclusions about the behavior of households with income variation.
Keywords: structural relation, robust estimation, least-squares method, regression penalized spline, Engel curve, budget survey. 
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V. I. Denisov; A. Yu. Timofeeva; E. A. Khailenko; O. I. Buzmakova. Robust estimation of nonlinear structural models. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 47-60. http://geodesic.mathdoc.fr/item/SJIM_2013_16_4_a4/

[1] Aivazyan S. A., Enyukov I. S., Meshalkin L. D., Prikladnaya statistika: issledovanie zavisimostei, Finansy i statistika, M., 1985 | MR

[2] Kendall M., Styuart A., Statisticheskie vyvody i svyazi, Nauka, M., 1973 | Zbl

[3] Berry S. M., Carroll R. J., Ruppert D., “Bayesian smoothing and regression splines for measurement error problems”, J. Amer. Statist. Assoc., 97:457 (2002), 160–169 | DOI | MR | Zbl

[4] Cheng C.-L., Schneeweiss H., “Polynomial regression with errors in the variables”, J. Roy. Statist. Soc. Ser. B, 60 (1998), 189–199 | DOI | MR | Zbl

[5] Greshilov A. A., Stakun V. A., Stakun A. A., Matematicheskie metody postroeniya prognozov, Radio i svyaz, M., 1997

[6] Ruppert D., Wand M. P., Carroll R. J., Semiparametric Regression, Cambridge Univ. Press, N.Y., 2003 | MR | Zbl

[7] Timofeeva A. Yu., Buzmakova O. I., “Poluparametricheskoe otsenivanie zavisimostei mezhdu stokhasticheskimi peremennymi”, Nauchn. vestn. NGTU, 49:4 (2012), 29–37

[8] Denisov V. I., Timofeev V. S., Buzmakova O. I., “Shtrafnye splainy v zadache identifikatsii poluparametricheskoi regressii”, Nauch. vestn. NGTU, 45:4 (2011), 11–24

[9] Timofeev V. S., Schekoldin V. Yu., Timofeeva A. Yu., “Identifikatsiya zavisimostei priznakov stokhasticheskoi prirody na osnove regressii Deminga”, Informatika i ee primeneniya, 7:2 (2013), 60–68

[10] Rousseeuw P. J., Van Driessen K., Computing LTS Regression for Large Data Sets, Antwerpen, 1999

[11] Denisov V. I., Timofeev V. S., “Issledovanie vliyaniya grubykh oshibok nablyudenii na informatsionnuyu matritsu Fishera”, Sib. zhurn. industr. matematiki, 11:2(34) (2008), 65–73 | MR | Zbl

[12] Denisov V. I., Timofeev V. S., Khailenko E. A., “Planirovanie utochnyayuschikh nablyudenii pri kontrollinge vozdushnykh linii po dannym lazernogo skanirovaniya”, Sib. zhurn. industr. matematiki, 15:2(50) (2012), 75–85

[13] Banks J., Blundell R., Lewbel A., “Quadratic Engel curves and consumer demand”, Rev. Econom. Statis., 79:4 (1997), 527–539 | DOI

[14] Kedir A., Girma S., “Quadratic Engel curves with measurement error: evidence from a budget survey”, Oxford Bull. Econom. Statist., 69:1 (2007), 123–138 | DOI

[15] Rousseeuw P. J., Croux C., “Alternatives to the median absolute deviation”, J. Amer. Statist. Assoc., 88:424 (1993), 1273–1283 | DOI | MR | Zbl

[16] Rossiiskii monitoring ekonomicheskogo polozheniya i zdorovya naseleniya NIU VShE (RLMS-HSE), URL: http://www.hse.ru/rlms/

[17] Kolesnikova A. Yu., Timofeev V. S., “Identifikatsiya modelei zavisimosti sprosa ot dokhoda v ramkakh neoklassicheskoi teorii”, Dokl. AN vysshei shkoly RF, 13:2 (2009), 51–65