Flexible Statistical Methods for Complex Structured Data Analysis

复杂的结构化数据来自许多领域，包括医学、工业和环境研究。因此，迫切需要开发强大的统计方法，以便能够更有效地利用信息，并使用更灵活的统计模型来分析数据。最具挑战性的统计问题之一是确定结果和风险因素之间的关系，并将结果模型用于结果预测。这方面的研究已经引起了广泛的关注，使用半参数或非参数方法的文献迅速增长，但灵活的方法来结合各种类型的风险影响仍然是非常需要的。 这项研究的主要目标是开发连贯的、新颖的方法来处理具有复杂结构的数据。我打算通过使用灵活的基于核机器的方法来为这一领域做出贡献，开发新的方法来促进响应和协变量之间的复杂关系，并为单一或多个结果数据构建预测模型。将开发变量选择方法以适应高维协变量数据。基于核机的方法允许比通常使用的线性关系更灵活的关系。此外，该方法的实现在计算上是有效的。基于核机方法开发的预测模型将具有比现有模型更好的预测精度。

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.