Bayes unbiased estimators of parameters of linear trend with autoregressive errors
Applications of Mathematics, Tome 32 (1987) no. 6, pp. 451-458
The method of least wquares is usually used in a linear regression model $\bold {Y=X\beta+\epsilon}$ for estimating unknown parameters $\bold \beta$. The case when $\epsilon$ is an autoregressive process of the first order and the matrix $\bold X$ corresponds to a linear trend is studied and the Bayes approach is used for estimating the parameters $\bold \beta$. Unbiased Bayes estimators are derived for the case of a small number of observations. These estimators are compared with the locally best unbiased ones and with the usual least squares estimators.
The method of least wquares is usually used in a linear regression model $\bold {Y=X\beta+\epsilon}$ for estimating unknown parameters $\bold \beta$. The case when $\epsilon$ is an autoregressive process of the first order and the matrix $\bold X$ corresponds to a linear trend is studied and the Bayes approach is used for estimating the parameters $\bold \beta$. Unbiased Bayes estimators are derived for the case of a small number of observations. These estimators are compared with the locally best unbiased ones and with the usual least squares estimators.
DOI :
10.21136/AM.1987.104276
Classification :
62F10, 62F15, 62J05, 62M10
Keywords: autoregressive process of first order; linear trend; Unbiased Bayes estimators; locally best unbiased; least squares estimators
Keywords: autoregressive process of first order; linear trend; Unbiased Bayes estimators; locally best unbiased; least squares estimators
@article{10_21136_AM_1987_104276,
author = {\v{S}tulajter, Franti\v{s}ek},
title = {Bayes unbiased estimators of parameters of linear trend with autoregressive errors},
journal = {Applications of Mathematics},
pages = {451--458},
year = {1987},
volume = {32},
number = {6},
doi = {10.21136/AM.1987.104276},
mrnumber = {0916061},
zbl = {0632.62091},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104276/}
}
TY - JOUR AU - Štulajter, František TI - Bayes unbiased estimators of parameters of linear trend with autoregressive errors JO - Applications of Mathematics PY - 1987 SP - 451 EP - 458 VL - 32 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104276/ DO - 10.21136/AM.1987.104276 LA - en ID - 10_21136_AM_1987_104276 ER -
%0 Journal Article %A Štulajter, František %T Bayes unbiased estimators of parameters of linear trend with autoregressive errors %J Applications of Mathematics %D 1987 %P 451-458 %V 32 %N 6 %U http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104276/ %R 10.21136/AM.1987.104276 %G en %F 10_21136_AM_1987_104276
Štulajter, František. Bayes unbiased estimators of parameters of linear trend with autoregressive errors. Applications of Mathematics, Tome 32 (1987) no. 6, pp. 451-458. doi: 10.21136/AM.1987.104276