Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 44). Also available in electronic version. Access restricted to campus users.

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published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

High breakdown point, bounded influence and high efficiency at the Gaussian model are desired properties of robust regression estimators. Robustness of validity, robustness of efficiency and high breakdown point size and power are the fundamental goals in robust testing. The objective of this dissertation is to examine the finite-sample properties of robust estimators and tests, and to find some useful applications for them. This is accomplished by extensive Monte Carlo experiments and other inference techniques in various contamination situations. In the linear regression model with an outlying regressor and deviations from the normal error distribution, robust estimators demonstrate noticeable advantages over the standard LS and maximum likelihood (ML) estimators. Our findings reveal that the finite-sample behavior of the robust estimators is very different from their asymptotic properties. The robust properties of estimators carry over to test statistics based on these estimators. The robust tests we proposed can achieve to the large extent the fundamental goals in robust testing. Economic applications on modelling the household consumption behavior and testing for (G)ARCH effects show that one can capture big gains from the appropriate utilization of the robust methods even at very simple models.

Multiple linear regression is a widely used statistical method. Its application, especially in the sciences, social sciences, and economics assists administrators in evaluating programs and planners in predicting future situations. The method is so common that most institutions have in their computer operation some standard programs to deal with the calculations. These traditional approaches use the method of least squares and yield an unbiased estimate of the parameters. The general linear model used is Y = Xβ+ e, where E(e) = 0, E(ee`) = σ2In and X is (n x p) and full rank. The least squares estimate of the unknown parameter vector β is then given by β = (X'X)-1X̀Y. This approach, however, often produces unsatisfactory (or even inaccurate) results if the data vectors are ill-conditioned. Such ill-conditioning is a result of non-orthogonal data vectors and inter-correlation of response variables that are unfortunately quite common in all fields.In recent years it has become obvious that for these applications the unbiased estimate is not necessarily the best over-all in terms of mean square error. A biased estimate may actually be of more value in analysis and prediction. Ridge estimators are biased estimators that have proved useful in these cases. In their basic form β(k) = [(X'X) + kI]-1 X́Y, they differ from the least squares estimator in that they have a small positive constant added to the diagonal elements of the X́X matrix.This thesis will first deal with the situations in which the least squares approach is not adequate and the cases where the ridge estimate contributes to a usable solution. The significant work which has been done in the field will be surveyed and the main problem of determining an appropriate constant k for the ridge estimate will be considered.

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Previous research that has evaluated the effectiveness of personality variables for predicting work performance has predominantly relied on methods designed to detect simple relationships. The research reported in this thesis employed artificial neural networks ??? a method that is capable of capturing complex nonlinear and configural relationships among variables ??? and the findings were compared to those obtained by the more traditional method of linear regression. Six datasets that comprise a range of occupations, personality inventories, and work performance measures were used as the basis of the analyses. A series of studies were conducted to compare the predictive performance of prediction equations that a) were developed using either artificial neural networks or linear regression, and b) differed with respect to the type and number of personality variables that were used as predictors of work performance. Studies 1 and 2 compared the two methods using individual personality variables that assess the broad constructs of the five-factor model of personality. Studies 3 and 4 used combinations of these broad variables as the predictors. Study 5 employed narrow personality variables that assess specific facets of the broad constructs. Additional methodological contributions include the use of a resampling procedure, the use of multiple measures of predictive performance, and the comparison of two procedures for developing neural networks. Across the studies, it was generally found that the neural networks were rarely able to outperform the simpler linear regression equations, and this was attributed to the lack of reliable nonlinearity and configurality in personality-work performance relationships. However, the neural networks were able to outperform linear regression in the few instances where there was some independent evidence of nonlinear or configural relationships. Consequently, although the findings do not support the usefulness of neural networks for specifically improving the effectiveness of personality variables as predictors of work performance, in a broader sense they provide some grounds for optimism for organisational researchers interested in applying this method to investigate and exploit complex relationships among variables.

This thesis considers location and scale parameter modelling of the heteroscedastic t-distribution. This new distribution is an extension of the heteroscedastic Gaussian and provides robust analysis in the presence of outliers as well accommodates possible heteroscedasticity by flexibly modelling the scale parameter using covariates existing in the data. To motivate components of work in this thesis the Gaussian linear mixed model is reviewed. The mixed model equations are derived for the location fixed and random effects and this model is then used to introduce Restricted Maximum Likelihood ( REML ). From this an algorithmic scheme to estimate the scale parameters is developed. A review of location and scale parameter modelling of the heteroscedastic Gaussian distribution is presented. In this thesis, the scale parameters are a restricted to be a function of covariates existing in the data. Maximum Likelihood ( ML ) and REML estimation of the location and scale parameters is derived as well as an efficient computational algorithm and software are presented. The Gaussian model is then extended by considering the heteroscedastic t distribution. Initially, the heteroscedastic t is restricted to known degrees of freedom. Scoring equations for the location and scale parameters are derived and their intimate connection to the prediction of the random scale effects is discussed. Tools for detecting and testing heteroscedasticity are also derived and a computational algorithm is presented. A mini software package " hett " using this algorithm is also discussed. To derive a REML equivalent for the heteroscedastic t asymptotic likelihood theory is discussed. In this thesis an integral approximation, the Laplace approximation, is presented and two examples, with the inclusion of ML for the heteroscedastic t, are discussed. A new approximate integral technique called Partial Laplace is also discussed and is exemplified with linear mixed models. Approximate marginal likelihood techniques using Modified Profile Likelihood ( MPL ), Conditional Profile Likelihood ( CPL ) and Stably Adjusted Profile Likelihood ( SAPL ) are also presented and offer an alternative to the approximate integration techniques. The asymptotic techniques are then applied to the heteroscedastic t when the degrees of freedom is known to form two distinct REMLs for the scale parameters. The first approximation uses the Partial Laplace approximation to form a REML for the scale parameters, whereas, the second uses the approximate marginal likelihood technique MPL. For each, the estimation of the location and scale parameters is discussed and computational algorithms are presented. For comparison, the heteroscedastic t for known degrees of freedom using ML and the two new REML equivalents are illustrated with an example and a comparative simulation study. The model is then extended to incorporate the estimation of the degrees of freedom parameter. The estimating equations for the location and scale parameters under ML are preserved and the estimation of the degrees of freedom parameter is integrated into the algorithm. The approximate REML techniques are also extended. For the Partial Laplace approximation the estimation of the degrees of freedom parameter is simultaneously estimated with the scale parameters and therefore the algorithm differs only slightly. The second approximation uses SAPL to estimate the parameters and produces approximate marginal likelihoods for the location, scale and degrees of freedom parameters. Computational algorithms for each of the techniques are also presented. Several extensive examples, as well as a comparative simulation study, are used to illustrate ML and the two REML equivalents for the heteroscedastic t with unknown degrees of freedom. The thesis is concluded with a discussion of the new techniques derived for the heteroscedastic t distribution along with their advantages and disadvantages. Topics of further research are also discussed. / Thesis (Ph.D.)--School of Agriculture and Wine, 2005.

Previous research that has evaluated the effectiveness of personality variables for predicting work performance has predominantly relied on methods designed to detect simple relationships. The research reported in this thesis employed artificial neural networks ??? a method that is capable of capturing complex nonlinear and configural relationships among variables ??? and the findings were compared to those obtained by the more traditional method of linear regression. Six datasets that comprise a range of occupations, personality inventories, and work performance measures were used as the basis of the analyses. A series of studies were conducted to compare the predictive performance of prediction equations that a) were developed using either artificial neural networks or linear regression, and b) differed with respect to the type and number of personality variables that were used as predictors of work performance. Studies 1 and 2 compared the two methods using individual personality variables that assess the broad constructs of the five-factor model of personality. Studies 3 and 4 used combinations of these broad variables as the predictors. Study 5 employed narrow personality variables that assess specific facets of the broad constructs. Additional methodological contributions include the use of a resampling procedure, the use of multiple measures of predictive performance, and the comparison of two procedures for developing neural networks. Across the studies, it was generally found that the neural networks were rarely able to outperform the simpler linear regression equations, and this was attributed to the lack of reliable nonlinearity and configurality in personality-work performance relationships. However, the neural networks were able to outperform linear regression in the few instances where there was some independent evidence of nonlinear or configural relationships. Consequently, although the findings do not support the usefulness of neural networks for specifically improving the effectiveness of personality variables as predictors of work performance, in a broader sense they provide some grounds for optimism for organisational researchers interested in applying this method to investigate and exploit complex relationships among variables.