Remarks on invariance principle for one-parametric recursive residuals

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Remarks on invariance principle for one-parametric recursive residuals. / Sakhanenko, A. I.; Kovalevskii, A. P.; Shelepova, A. D.

в: Siberian Electronic Mathematical Reports, Том 18, № 2, 40, 2021, стр. 1058-1074.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{d66455e7a2df4f0883199b229e509990,

title = "Remarks on invariance principle for one-parametric recursive residuals",

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, Durb{\"i}n 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.",

keywords = "linear regression, recursive residuals, weak convergence, Wiener process.",

author = "Sakhanenko, {A. I.} and Kovalevskii, {A. P.} and Shelepova, {A. D.}",

note = "Funding Information: Sakhanenko, A.I., Kovalevskii, A.P., Shelepova, A.D., Remarks on invariance principle for one-parametric recursive residuals. {\textcopyright} 2021 Sakhanenko A.I., Kovalevskii A.P., Shelepova A.D. The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation. Received August, 29, 2021, published October, 20, 2021. Publisher Copyright: {\textcopyright} 2021. Sakhanenko A.I., Kovalevskii A.P., Shelepova A.D.",

year = "2021",

doi = "10.33048/SEMI.2021.18.081",

language = "English",

volume = "18",

pages = "1058--1074",

journal = "Сибирские электронные математические известия",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

number = "2",

}

RIS

TY - JOUR

T1 - Remarks on invariance principle for one-parametric recursive residuals

AU - Sakhanenko, A. I.

AU - Kovalevskii, A. P.

AU - Shelepova, A. D.

N1 - Funding Information: Sakhanenko, A.I., Kovalevskii, A.P., Shelepova, A.D., Remarks on invariance principle for one-parametric recursive residuals. © 2021 Sakhanenko A.I., Kovalevskii A.P., Shelepova A.D. The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation. Received August, 29, 2021, published October, 20, 2021. Publisher Copyright: © 2021. Sakhanenko A.I., Kovalevskii A.P., Shelepova A.D.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - linear regression

KW - recursive residuals

KW - weak convergence

KW - Wiener process.

UR - http://www.scopus.com/inward/record.url?scp=85120952181&partnerID=8YFLogxK

U2 - 10.33048/SEMI.2021.18.081

DO - 10.33048/SEMI.2021.18.081

M3 - Article

AN - SCOPUS:85120952181

VL - 18

SP - 1058

EP - 1074

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

M1 - 40

ER -

ID: 34952254