# Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors

Applications of Mathematics (1991)

- Volume: 36, Issue: 2, page 149-155
- ISSN: 0862-7940

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topŠtulajter, František. "Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors." Applications of Mathematics 36.2 (1991): 149-155. <http://eudml.org/doc/15667>.

@article{Štulajter1991,

abstract = {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.},

author = {Štulajter, František},

journal = {Applications of Mathematics},

keywords = {stochastic process; least squares estimators; quadratic invariant estimators; linear regression model; unknown covariance function; sufficient condition for consistency; least squares invariant quadratic estimator; unknown covariance function; sufficient condition for consistency; linear regression model},

language = {eng},

number = {2},

pages = {149-155},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors},

url = {http://eudml.org/doc/15667},

volume = {36},

year = {1991},

}

TY - JOUR

AU - Štulajter, František

TI - Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors

JO - Applications of Mathematics

PY - 1991

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 36

IS - 2

SP - 149

EP - 155

AB - 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.

LA - eng

KW - stochastic process; least squares estimators; quadratic invariant estimators; linear regression model; unknown covariance function; sufficient condition for consistency; least squares invariant quadratic estimator; unknown covariance function; sufficient condition for consistency; linear regression model

UR - http://eudml.org/doc/15667

ER -

## References

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- E. Z. Demidenko, Linear and nonlinear regression, (Russian) Finansy i statistika, Moscow 1981. (1981) MR0628141
- E. J. Hannan, 10.2307/1426656, Advances Appl.. Prob. 10 (197S), 740-743. (197S) DOI10.2307/1426656
- V. Solo, 10.1214/aos/1176345476, Ann. Stat. 9 (1981), 689-693. (1981) Zbl0477.62048MR0615448DOI10.1214/aos/1176345476
- F. Štulajter, Estimators in random processes, (Slovak). Alfa, Bratislava 1989. (1989)
- 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. (1983) MR0704788

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