| 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:
|
http://hdl.handle.net/10338.dmlcz/104452 |
| . |
| 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 |
| . |
