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Probability theory and mathematical statistics
Remarks on invariance principle for one-parametric recursive residuals
A. Sakhanenkoab, A. Kovalevskiicb, A. Shelepovab a Sobolev Institute of Mathematics, 4, Acad. Koptyug ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
c Novosibirsk State Technical University, 20, K. Marksa ave., Novosibirsk, 630073, Russia
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, 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.
Received August 29, 2021, published October 20, 2021
Citation:
A. Sakhanenko, A. Kovalevskii, A. Shelepova, “Remarks on invariance principle for one-parametric recursive residuals”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1058–1074
Linking options:
https://www.mathnet.ru/eng/semr1422 https://www.mathnet.ru/eng/semr/v18/i2/p1058
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Abstract page: | 104 | Full-text PDF : | 30 | References: | 20 |
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