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Štulajter, František
Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors. (English). Applications of Mathematics, vol. 36 (1991), issue 2, pp. 149-155
MSC: 62J05, 62M10 | MR 1097699 | Zbl 0727.62087 | DOI: 10.21136/AM.1991.104452
Keywords:
stochastic process; least squares estimators; quadratic invariant estimators; linear regression model; unknown covariance function; sufficient condition for consistency
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.
References:
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[2] E. Z. Demidenko: Linear and nonlinear regression. (Russian) Finansy i statistika, Moscow 1981. MR 0628141
[3] E. J. Hannan: Rates of convergence for time series regression. Advances Appl.. Prob. 10 (197S), 740-743. DOI 10.2307/1426656
[4] V. Solo: Strong consistency of least squares estimators in regression with correlated disturbances. Ann. Stat. 9 (1981), 689-693. DOI 10.1214/aos/1176345476 | MR 0615448 | Zbl 0477.62048
[5] F. Štulajter: Estimators in random processes. (Slovak). Alfa, Bratislava 1989.
[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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