Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 519.7
NONPARAMETRIC ESTIMATION OF REGRESSION CURVES IN THE CONDITIONS OF LARGE SAMPLES
A. V. Lapko [1],[2], V. A. Lapko [1], [2], D. V. Borisov [1]
[1] Siberian State Aerospace University named after academician M. F. Reshetnev 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660014, Russian Federation Е-mail: valapko@yandex.ru [2]Institute of Computational Modeling, Siberian Branch of RAS 50, Akademgorodok, Krasnoyarsk, 660036, Russian Federation Е-mail: lapko@icm.krasn.ru
The technique of construction of a nonparametric regression in the conditions of training samples of large volume is offered. Model synthesis is based on decomposition of initial statistical data and the analysis of probabilistic characteristics of received random variables sets. Asymptotic properties of a nonparametric regression are investigated and results of computing experiment are considered. Association of nonparametric regression properties on an amount of sampling intervals of values of an random variable and volume of input datas is established. Comparison of approximating properties of offered model and a traditional nonparametric regression is spent. The results of re-searches are important to the solution of problems of a confidential estimation of a probability density and a regression curves.
nonparametric regression, probability density, regression estimations, approximating properties, sampling methods.
References
  1. Lapko A. V., Lapko V. A. Neparametricheskie sistemy obrabotki neodnorodnoj informacii (Nonparametric heterogeneous information processing system). Novosibirsk, Nauka, 2007. 174 p.
  2. Lapko V. A., Kapustin A. N. Avtometrija. 2006, vol. 42, no. 6, p. 26–33.
  3.  Lapko A. V., Lapko V. A., Egorochkin I. A. Sistemy upravlenija i informacionnye tehnologii. 2009, no. 1 (35), p. 60–64.
  4.  Lapko A. V., Lapko V. A. Vestnik SibGAU. 2010, no. 2 (28), p. 32–35.
  5.  Lapko A. V., Lapko V. A. Informatika i sistemy upravlenija. 2013, no. 1 (35), p. 119–126.
  6.  Lapko A. V., Lapko V. A. Informatika i sistemy upravlenija. 2012, no. 2, p. 121–126.
  7. Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologiju. 2011, vol. 43, no. 1, p. 12–15.
  8.  Lapko A. V., Lapko V. A. Avtometrija. 2010, vol. 46, no. 1, p. 70–78.
  9.  Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologii. 2009, no. 3.1 (37), p. 156–160.
  10.  Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologii. 2010, no. 1 (39), p. 16–19.
  11.  Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologii. 2010, no. 1.2 (39), p. 300–304.
  12.  Lapko A. V., Lapko V. A., Varochkin S. S. Vestnik SibGAU. 2009, no. 1 (22), рart 2, p. 38–40.
  13.  Lapko A. V., Lapko V. A. Vestnik SibGAU. 2012, no. 3 (43), p. 42–46.
  14. Lapko A. V., Lapko V. A. Sistemy upravlenija i informacionnye tehnologii. 2012, vol. 49, no. 3, p. 152–156.
  15.  Lapko A. V., Lapko V. A. Avtometrija. 2003, vol. 39 no. 1, p. 54–61.
  16.  Lapko A. V., Lapko V. A. Informatika i sistemy upravlenija. 2013, no. 4 (38), p. 63–69.
  17.  Lapko A. V., Lapko V. A. Metrologija. 2013, no. 12, p. 3–9.
  18.  Lapko A. V., Lapko V. A. Izmeritel'naja tehnika. 2013, no. 7, p. 24–27.
  19. Lapko A. V., Lapko V. A. Optimal selection of the number of sampling intervals in domain of variation of a one-dimensional random variable in estimation of the probability density. Measurement Techniques, 2013, vol. 56, no. 7, p. 24 – 27. doi: 10.1007/s11018-013-0279-x.
  20.  Nadaraja Je. A. Teorija verojatnosti i ejo primenenija. 1970, vol. 15, no. 1, p. 139–142.
  21. Hardle V. Prikladnaja neparametricheskaja regressija (Applied nonparametric regression). Moscow, Mir, 1993. 300 p.
  22.  Epanechnikov V. A. Teorija verojatnosti i ee primenenija. 1969, vol. 14, no. 1, p. 156–161.

 


Lapko Alexander Vasilyevich – Doctor of Engineering Science, professor, Leading researcher of Institute of Computational Modelling of Russian Academy of Sciences, Siberian Branch, professor of the Space craft and Technologies Department, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: lapko@icm.krasn.ru gineer� Si�`P 0�K sociate professor, Leading researcher of Institute of Computational Modelling of the Russian Academy of Sciences, Siberian Branch, head of the Space craft and Technologies Department, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: valapko@yandex.ru

Lapko Vasily Alexandrovich – Doctor of Engineering Sciences, associate professor, Leading researcher of Institute of Computational Modelling of the Russian Academy of Sciences, Siberian Branch, head of the Space craft and Technologies Department, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: valapko@yandex.ru

Borisov Dmitry Vladimirovich – Student, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: dimbo2007@yandex.ru