Average quadratic error of the estimate of the first order splines in the model of linear regression
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...
Збережено в:
| Дата: | 1991 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1991
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/9628 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513545382264832 |
|---|---|
| author | Petunina , M. Yu. Петунина , М. Ю. |
| author_facet | Petunina , M. Yu. Петунина , М. Ю. |
| author_sort | Petunina , M. Yu. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-10-09T12:05:28Z |
| description | 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. |
| first_indexed | 2026-03-24T03:46:23Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-9628 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:46:23Z |
| publishDate | 1991 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/2d/7c75b9aa9ca8b73f51db4ce133da5a2d |
| spelling | umjimathkievua-article-96282025-10-09T12:05:28Z Average quadratic error of the estimate of the first order splines in the model of linear regression Средняя квадратическая ошибка оценки сплайнов первого порядка в модели линейной регрессии Petunina , M. Yu. Петунина , М. Ю. - 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. Изучается средняя квадратическая ошибка оценки сплайнов первого порядка, полученной методом наименьших квадратов при условии, что наблюдения представляют суперпозицию истинных значений сплайна и белого шума. Найдена формула для вычисления средней квадратической ошибки и исследована ее асимптотика. Вивчається середня квадратична похибка оцінки сплайнів першого порядку, одержаної методом найменших квадратів за умови, що спостереження становлять суперпозицію істинних значень сплайн та білого шуму. Знайдена формула для обчислення середньої квадратичної похибки і досліджена її асимптотика. Institute of Mathematics, NAS of Ukraine 1991-02-28 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9628 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 3 (1991); 429-432 Український математичний журнал; Том 43 № 3 (1991); 429-432 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9628/10596 Copyright (c) 1991 М. Ю. Петунина |
| spellingShingle | Petunina , M. Yu. Петунина , М. Ю. Average quadratic error of the estimate of the first order splines in the model of linear regression |
| title | Average quadratic error of the estimate of the first order splines in the model of linear regression |
| title_alt | Средняя квадратическая ошибка оценки сплайнов первого порядка в модели линейной регрессии |
| title_full | Average quadratic error of the estimate of the first order splines in the model of linear regression |
| title_fullStr | Average quadratic error of the estimate of the first order splines in the model of linear regression |
| title_full_unstemmed | Average quadratic error of the estimate of the first order splines in the model of linear regression |
| title_short | Average quadratic error of the estimate of the first order splines in the model of linear regression |
| title_sort | average quadratic error of the estimate of the first order splines in the model of linear regression |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9628 |
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