Limit theorems for the maximal residuals in linear and nonlinear regression models
Authors:
A. V. Ivanov and I. K. Matsak
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 86 (2013), 79-91
MSC (2010):
Primary 60G70, 62J05
DOI:
https://doi.org/10.1090/S0094-9000-2013-00890-4
Published electronically:
August 20, 2013
MathSciNet review:
2986451
Full-text PDF Free Access
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Additional Information
Abstract: Limit theorems for the maximal residuals in linear and nonlinear regression models are obtained in the paper. An application of the main result for constructing a regression model adequacy test is given.
References
- G. A. F. Seber, Linear regression analysis, John Wiley & Sons, New York-London-Sydney, 1977. Wiley Series in Probability and Mathematical Statistics. MR 0436482
- Alexander V. Ivanov, Asymptotic theory of nonlinear regression, Mathematics and its Applications, vol. 389, Kluwer Academic Publishers Group, Dordrecht, 1997. MR 1472234
- B. Gnedenko, Sur la distribution limite du terme maximum d’une série aléatoire, Ann. of Math. (2) 44 (1943), 423–453 (French). MR 8655, DOI https://doi.org/10.2307/1968974
- Janos Galambos, The asymptotic theory of extreme order statistics, John Wiley & Sons, New York-Chichester-Brisbane, 1978. Wiley Series in Probability and Mathematical Statistics. MR 489334
- Sidney I. Resnick, Extreme values, regular variation, and point processes, Applied Probability. A Series of the Applied Probability Trust, vol. 4, Springer-Verlag, New York, 1987. MR 900810
- M. R. Leadbetter, Georg Lindgren, and Holger Rootzén, Extremes and related properties of random sequences and processes, Springer Series in Statistics, Springer-Verlag, New York-Berlin, 1983. MR 691492
- Eugene Seneta, Regularly varying functions, Lecture Notes in Mathematics, Vol. 508, Springer-Verlag, Berlin-New York, 1976. MR 0453936
- E. Malinvaud, The consistency of nonlinear regressions, Ann. Math. Statist. 41 (1970), 956–969. MR 261754, DOI https://doi.org/10.1214/aoms/1177696972
References
- G. A. F. Seber, Linear Regression Analysis, Wiley, New York, 1977. MR 0436482 (55:9428)
- A. V. Ivanov, Asymptotic Theory of Nonlinear Regression, Kluwer Academic Press, Dordrecht, 1997. MR 1472234 (99h:62086)
- B. V. Gnedenko, Sur la distribution limit du terme maximum d‘une serie aleatoire, Ann. Math. 44 (1943), 423–453. MR 0008655 (5:41b)
- J. Galambos, The Asymptotic Theory of Extreme Order Statistics, John Wiley & Sons, New York–Chichester–Brisbane, 1978. MR 489334 (80b:60040)
- S. I. Resnick, Extreme Values, Regular Variation and Point Processes, Springer, Berlin, 1987. MR 900810 (89b:60241)
- M. R. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York–Heidelberg–Berlin, 1983. MR 691492 (84h:60050)
- E. Seneta, Regularly Varying Functions, Springer-Verlag, Berlin–Heidelberg–New York, 1976. MR 0453936 (56:12189)
- E. Malinvaud, The Consistency of Nonlinear Regression, Ann. Math. Statist. 41 (1970), 953–969. MR 0261754 (41:6367)
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Additional Information
A. V. Ivanov
Affiliation:
National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremogy Avenue, 37, Kyiv 03056, Ukraine
Email:
alexntuu@gmail.com
I. K. Matsak
Affiliation:
Kyiv National Taras Shevchenko University, Glushkov Avenue 2,Building 6, Kyiv 03127, Ukraine
Email:
mik@unicyb.kiev.ua
Keywords:
Regression model,
maximal error,
regression model adequacy test
Received by editor(s):
October 9, 2011
Published electronically:
August 20, 2013
Article copyright:
© Copyright 2013
American Mathematical Society
