Geodesic
Remarks on invariance principle for one-parametric recursive residuals
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1058-1074

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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, Durbin 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. 
@article{SEMR_2021_18_2_a20,
     author = {A. Sakhanenko and A. Kovalevskii and A. Shelepova},
     title = {Remarks on invariance principle for one-parametric recursive residuals},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1058--1074},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a20/}
}
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A. Sakhanenko; A. Kovalevskii; A. Shelepova. Remarks on invariance principle for one-parametric recursive residuals. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1058-1074. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a20/