M.Sc. / In this study we consider the problem ofestiniating the slope in the simple linear errors-in-variables model. There are two different types of relationship that can he specified in the errors-in-variables model: one that specifies a functional linear relationship and one describing a structural linear relationship. The different relationship specifications can lead to different estimators with different properties. These two specifications are highlighted in this study. A least squares solution (to the estimation of the slope) is given. The problem of finding the maximum likelihood solution to these two specifications is addressed. It is noted that an unidentifiability problem arises in this attempt. The solution is seen to lie in making assumptions on the error variances. Interval estimation for the slope parameter is discussed. It is noted that any interval estimator of the slope whose length is always finite will have a confidence coefficient of zero. Various interval estimation methods are reviewed but emphasis is mainly on the investigation of a bootstrap procedure for estimating the confidence interval for the slope parameter β. More specifically, the Linder and Babu (1994) (bootstrap) method for the structural relationship model with known variance ratio is investigated here. The error distributions were assumed normal. A simulation study based on this paper is carried out. The results in the simulation study show that this bootstrap procedure performs well in comparison with the normal theory estimates for normally distributed data, that is, it has better coverage accuracy than the normal approximation.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uj/uj:9028 |
| Date | 13 August 2012 |
| Creators | Musekiwa, Alfred. |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Thesis |
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