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

František Štulajter

Applications of Mathematics (1991)

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

Abstract

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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.

How to cite

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Štulajter, 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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  1. T. W. Anderson J. B. Taylor, 10.1214/aos/1176343552, Ann. Stat. 4 (1976), 788-790. (1976) Zbl0339.62039MR0415899DOI10.1214/aos/1176343552
  2. E. Z. Demidenko, Linear and nonlinear regression, (Russian) Finansy i statistika, Moscow 1981. (1981) MR0628141
  3. E. J. Hannan, 10.2307/1426656, Advances Appl.. Prob. 10 (197S), 740-743. (197S) Zbl0394.62068DOI10.2307/1426656
  4. V. Solo, 10.1214/aos/1176345476, Ann. Stat. 9 (1981), 689-693. (1981) Zbl0477.62048MR0615448DOI10.1214/aos/1176345476
  5. F. Štulajter, Estimators in random processes, (Slovak). Alfa, Bratislava 1989. (1989) Zbl0698.62087
  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. (1983) Zbl0545.60027MR0704788

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