REMARKS ON INVARIANCE PRINCIPLE FOR ONE-PARAMETRIC RECURSIVE RESIDUALS | Sciact - Система учета научной деятельности ИМ СО РАН

REMARKS ON INVARIANCE PRINCIPLE FOR ONE-PARAMETRIC RECURSIVE RESIDUALS Научная публикация

Журнал

Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304

Вых. Данные

Год: 2021, Том: 18, Номер: 2, Страницы: 1058-1074 Страниц : 17 DOI: 10.33048/SEMI.2021.18.081

Ключевые слова

linear regression; recursive residuals; weak convergence; Wiener process.

Авторы

Sakhanenko A.I. ^1,2 , Kovalevskii A.P. ^2,3 , Shelepova A.D. ²

Организации

1	Sobolev Institute of Mathematics, 4, Acad. Koptyug ave, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, 1, Pirogava str, Novosibirsk, 630090, Russian Federation
3	Novosibirsk State Technical University, 20, K. Marksa ave., Novosibirsk, 630073, Russia

Информация о финансировании (1)

Математический центр в Академгородке

075-15-2019-1675

We investigate a linear regression model with one unknown parameter. The idea of recursive regression residuals is to estimate the regression parameter at each moment on the base of previous variables. Therefore the distribution of recursive residuals does not depend on the parameter. We investigate conditions for the weak convergence of the process of sums of recursive residuals, properly normalized, to a standard Wiener process. We obtain new conditions, which are better than ones in Sen (1982). The recursive residuals were introduced by Brown, Durbïn and Evans (1975). Such residuals are the useful instrument for testing hypotheses about linear regression. Our results give opportunity to use correctly recursive residuals for a wide class of regression sequences, including sinusoidal and i.i.d. bounded. © 2021. Sakhanenko A.I., Kovalevskii A.P., Shelepova A.D.

Sakhanenko A.I. , Kovalevskii A.P. , Shelepova A.D.
REMARKS ON INVARIANCE PRINCIPLE FOR ONE-PARAMETRIC RECURSIVE RESIDUALS
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2021. V.18. N2. P.1058-1074. DOI: 10.33048/SEMI.2021.18.081 WOS Scopus OpenAlex

Web of science:	WOS:000734395000001
Scopus:	2-s2.0-85120952181
OpenAlex:	W3213482400

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