Improved estimation of the parameters of simple linear regression model with autocorrelated errors

 

A.K.Md.E. Saleh, F. Tang, and B.M.G. Kibria (2009). Improved estimation of the parameters of simple linear regression model with autocorrelated errors. Journal of Statistical Research, Vol. 43, No. 1, pp.  89-107.

 

Abstract

The problem of estimating the parameters of a simple linear regression model with known autocorrelated errors is the main concern of this paper. We consider the unrestricted estimator, restricted estimator, preliminary test estimator (PTE) and shrinkage estimator (SE) of the parameters $ \theta $ and $ \beta $. The bias and MSE expressions of the proposed estimators are given and analyzed. From the study of some graphs and efficiency tables, it is evident that the proposed preliminary test and shrinkage estimators dominate the unrestricted estimator for some values of $ \Delta $. Sample tables of maximum/minimum efficiencies are provided for various $ \rho $ and level of significance values to assess the performance of the estimators and choose optimum levels of significance of the PTE. For small size of the test, the SE performs better than the PT estimator, while for larger sizes, the PT performs better than the SE.

 

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