Flexible Statistical Methods for Complex Structured Data Analysis

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Complex structured data emerge from many fields including medical, industrial and environmental studies. Consequently, there is an urgent need for developing powerful statistical methods to enable more efficient use of information, and to analyze data using more flexible statistical models. One of the most challenging statistical issues is identification of the relationship between outcomes and risk factors, and ultilization of the resulting models for outcome prediction. Extensive research attention has been directed to this area and there has been a rapid growth in the literature using either semi-parametric or nonparametric approaches, but flexible approaches to incorporate various types of risk effects are still in great demand. The primary objective of this research is to develop coherent and novel methodology to deal with data with complex structures. I intend to contribute to this area by employing flexible kernel machine based methods, to develop new methods to facilitate complex relationships between a response and covariates, and to construct predictive models for either single or multiple outcome data. Variable selection methods will be developed to accommodate high dimensional covariate data. The kernel machine based approach allows a more flexible relationship than commonly used linear relationships. Furthermore, the implementation of this method can be made computationally efficient. The predictive models to be developed based on the kernel machine approaches will enjoy better prediction accuracy than existing models.