Sciact
  • EN
  • RU

REMARKS ON INVARIANCE PRINCIPLE FOR ONE-PARAMETRIC RECURSIVE RESIDUALS Full article

Journal Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304
Output data Year: 2021, Volume: 18, Number: 2, Pages: 1058-1074 Pages count : 17 DOI: 10.33048/SEMI.2021.18.081
Tags linear regression; recursive residuals; weak convergence; Wiener process.
Authors Sakhanenko A.I. 1,2 , Kovalevskii A.P. 2,3 , Shelepova A.D. 2
Affiliations
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

Funding (1)

1 Mathematical Center in Akademgorodok 075-15-2019-1675

Abstract: 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.
Cite: 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
Identifiers:
Web of science: WOS:000734395000001
Scopus: 2-s2.0-85120952181
OpenAlex: W3213482400
Citing: Пока нет цитирований
Altmetrics: