Most traditional parametric and nonparametric regression methods operate under the assumption that the true function is continuous over the design space. For methods such as ordinary least squares polynomial regression and local polynomial regression the functional estimates are constrained to...

The generalized linear model (GLM) is a popular model in many research areas. In theGLM, each outcome of the dependent variable is assumed to be generated from a particulardistribution function in the exponential family. The mean of the distribution depends onthe independent variables. The link...

In typical normal theory regression, the assumption ofhomogeneity of variances is often not appropriate.Instead of treating the variances as a nuisance andtransforming away the heterogeneity, the structure ofthe variances may be of interest and it is desirable tomodel the variances. Aitkin...

Time Series of water quality variables typically possess many of several characteristics which complicate analysis. Of interest to researchers is often the trend over time of the water quality variable. However, sometimes water quality variable levels appear to increase or decrease monotonically...

One form of model robust regression (MRR) predicts mean response as a convexcombination of a parametric and a nonparametric prediction. MRR is a semiparametricmethod by which an incompletely or an incorrectly specified parametric model can beimproved through adding an appropriate amount of a...

There is a growing interest in robust and nonparametric methods with engineering applications, due to the nature of the data. Here, we study two power systems engineering applications that employ or recommend robust and nonparametric methods; topology error identification and voltage...

The standard methodology when building statistical models has been to use one of several algorithms to systematically search the model space for a good model. If the number of variables is small then all possible models or best subset procedures may be used, but for data sets with a large number...

The content of this dissertation is divided into two main topics: 1) nonlinear profilemonitoring and 2) an improved approximate distribution for the T^2 statistic based on thesuccessive differences covariance matrix estimator. (Part 1) In an increasing number of cases the quality of a product or...

Mixed models are powerful tools for the analysis of clustered data and many extensions of the classical linear mixed model with normally distributed response have been established. As with all parametric models, correctness of the assumed model is critical for the validity of the ensuing...

Interest in transform methods for normalising test statistics declined with the advent of computers. More recently, small-sample asymptotic methods have been developed to approximate the distributions of complicated test statistics. We propose a generalisation of a classical symmetrising...