Average quadratic error of the estimate of the first order splines in the model of linear regression

Authors

  • M. Yu. Petunina Ин-т математики АН УССР, Киев

Keywords:

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Abstract

We study the mean quadratic error of an estimate of splines of the first order, which is obtained by the method of least squares under the assumption that the data represents a superposition of proper values of a spline and a white noise. A quantitative formula for the quadratic mean error is found and its asymptotics is investigated.

References

1. Себер Дж. Линейный регрессионный анализ.— М. : Мир, 1980.— 456 с.

2. Завьялов Ю. С., Квасов Б. И., Мирошниченко В. Л. Методы сплайн-функций.—М. : Наука, 1980.— 352 с.

3. Проскуряков И. В. Сборник задач по линейной алгебре.— М. : Гостехтеоретиздат, 1957.— 368 с.

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Published

28.02.1991

Issue

Vol. 43 No. 3 (1991)

Section

Short communications

License

Copyright (c) 1991 М. Ю. Петунина

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Petunina , M. Yu. “Average Quadratic Error of the Estimate of the First Order Splines in the Model of Linear Regression”. Ukrains’kyi Matematychnyi Zhurnal, vol. 43, no. 3, Feb. 1991, pp. 429-32, https://umj.imath.kiev.ua/index.php/umj/article/view/9628.