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Keywords:
autoregressive process of first order; linear trend; Unbiased Bayes estimators; locally best unbiased; least squares estimators
autoregressive process of first order; linear trend; Unbiased Bayes estimators; locally best unbiased; least squares estimators
Summary:
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.
References:
[1] J. Anděl: Statistical Analysis of Time series. (Czech) SNTL, Praha 1976.
[2] C. R. Rao: Linear Statistical Inference and Its Applications. J. Wiley, N. York 1965. MR 0221616 | Zbl 0137.36203
[3] A. Zellner: An Introduction to Bayesian Inference in Econometric. J. Wiley, N. York 1971. MR 0433791
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