The performance of the preliminary test estimator under different loss functions

• Main Author: Kleyn, Judith
• Other Authors: Arashi, Mohammad
• Language: en
• Published: University of Pretoria 2015
• Subjects: Block bootstrapping; Bounded LINEX loss function; Feasible Bayes estimator; LINEX loss function; Preliminary test estimator; UCTD
• Online Access: http://hdl.handle.net/2263/43132; Kleyn, J 2014, The performance of the preliminary test estimator under different loss functions, PhD Thesis, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/43132>

In this thesis different situations are considered in which the preliminary test estimator is applied and the performance of the preliminary test estimator under different proposed loss functions, namely the reflected normal , linear exponential (LINEX) and bounded LINEX (BLINEX) loss functions is evaluated. In order to motivate the use of the BLINEX loss function rather than the reflected normal loss or the LINEX loss function, the risk for the preliminary test estimator and its component estimators derived under BLINEX loss is compared to the risk of the preliminary test estimator and its components estimators derived under both reflected normal loss and LINEX loss analytically (in some sections) and computationally. It is shown that both the risk under reflected normal loss and the risk under LINEX loss is higher than the risk under BLINEX loss. The key focus point under consideration is the estimation of the regression coefficients of a multiple regression model under two conditions, namely the presence of multicollinearity and linear restrictions imposed on the regression coefficients. In order to address the multicollinearity problem, the regression coefficients were adjusted by making use of Hoerl and Kennard’s (1970) approach in ridge regression. Furthermore, in situations where under- or overestimation exist, symmetric loss functions will not give optimal results and it was necessary to consider asymmetric loss functions. In the economic application, it was shown that a loss function which is both asymmetric and bounded to ensure a maximum upper bound for the loss, is the most appropriate function to use. In order to evaluate the effect that different ridge parameters have on the estimation, the risk values were calculated for all three ridge regression estimators under different conditions, namely an increase in variance, an increase in the level of multicollinearity, an increase in the number of parameters to be estimated in the regression model and an increase in the sample size. These results were compared to each other and summarised for all the proposed estimators and proposed loss functions. The comparison of the three proposed ridge regression estimators under all the proposed loss functions was also summarised for an increase in the sample size and an increase in variance. === Thesis (PhD)--University of Pretoria, 2014. === lk2014 === Statistics === PhD === Unrestricted