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Title: Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors (English)
Author: Štulajter, František
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 36
Issue: 2
Year: 1991
Pages: 149-155
Summary lang: English
Category: math
Summary: The least squres invariant quadratic estimator of an unknown covariance function of a stochastic process is defined and a sufficient condition for consistency of this estimator is derived. The mean value of the observed process is assumed to fulfil a linear regresion model. A sufficient condition for consistency of the least squares estimator of the regression parameters is derived, too. (English)
Keyword: stochastic process
Keyword: least squares estimators
Keyword: quadratic invariant estimators
Keyword: linear regression model
Keyword: unknown covariance function
Keyword: sufficient condition for consistency
MSC: 62J05
MSC: 62M10
idZBL: Zbl 0727.62087
idMR: MR1097699
DOI: 10.21136/AM.1991.104452
Date available: 2008-05-20T18:41:20Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] T. W. Anderson J. B. Taylor: Strong consistency of least squares estimates in normal linear regression.Ann. Stat. 4 (1976), 788-790. MR 0415899, 10.1214/aos/1176343552
Reference: [2] E. Z. Demidenko: Linear and nonlinear regression.(Russian) Finansy i statistika, Moscow 1981. MR 0628141
Reference: [3] E. J. Hannan: Rates of convergence for time series regression.Advances Appl.. Prob. 10 (197S), 740-743. 10.2307/1426656
Reference: [4] V. Solo: Strong consistency of least squares estimators in regression with correlated disturbances.Ann. Stat. 9 (1981), 689-693. Zbl 0477.62048, MR 0615448, 10.1214/aos/1176345476
Reference: [5] F. Štulajter: Estimators in random processes.(Slovak). Alfa, Bratislava 1989.
Reference: [6] R. Thrum J. Kleffe: Inequalities for moments of quadratic forms with applications to almost sure convergence.Math. Oper. Stat. Ser. Stat. 14 (1983), 211 - 216. MR 0704788


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