Data-Analytic Modeling for High-Dimensional Data

9803200fanjianqing本研究涉及多种新的数据分析技术，用于处理和建模高维数据，这些技术来自许多科学学科。这些应用包括流行病学和环境统计学的变系数模型，金融学的时间非均匀扩散模型，眼科、市场营销和生物统计学的曲线和图像数据，以及统计学和工程学中的小波应用。该研究大大提高了分析这些复杂高维数据的工具和软件的可用性。该研究涵盖了广泛的方法论发展和基础研究。特别关注四个相互关联的主题。首先，提出了一种两步法的变系数模型有效估计策略。当系数函数允许不同程度的平滑时，这是特别有用的。所提出的方法将通过仔细制定的渐近理论和模拟来证明。所提出的方法扩展到纵向研究和基于似然的模型，如广义线性模型。其次，提出了时间非齐次扩散模型来模拟期限结构动力学和资产定价。这些非参数模型旨在解决过度简化的参数模型的不足之处。提出了各种数据分析建模技术，并通过理论研究和实证研究进行了验证。第三，讨论了小波在各种统计问题中的应用。提出的方法从统计建模的角度出发，基于惩罚似然思想。我们的目标是扩大小波在统计中的适用性，并提高一些现有技术的效率。特别提出了基于似然的模型，鲁棒性，去噪相关数据和加性建模进行研究。最后，研究了处理曲线和图像数据时出现的一些统计推断问题。

9803200Jianqing FanThis research involves a variety of new data-analytic techniques for processing and modeling high dimensional data that arise from many scientific disciplines. These range from varying-coefficient models from epidemiology and environmental statistics, time-inhomogeneous diffusion models from finance, curves and images data from ophthalmology, marketing and biostatistics, to wavelet applications in statistics and engineering. The research enhances significantly the availability of tools and software for analyzing these complicated high-dimensional data.The research covers a wide array of methodological developments and foundational research. In particular, four inter-related topics are focussed. Firstly, a two-step strategy is proposed for efficient estimation in varying-coefficient models. This is particularly useful when coefficient functions admit different degrees of smoothness. The proposed methods will be justified by carefully formulated asymptotic theory and simulations. The proposed methods extends to longitudinal studies and likelihood-based models such as generalized linear models. Secondly, time-inhomogeneous diffusion models are proposed to model term-structure dynamics and asset pricing. These nonparametric models aim at addressing inadequacy of over simplified parametric models. Various data-analytic modeling techniques are proposed and justified by both theoretical studies and empirical research. Thirdly, wavelet applications to a variety of statistical problems are discussed. The proposed approaches derive from statistical modeling prospective and are based on penalized likelihood idea. Our aim is to expand the applicability of wavelets in statistics and to improve efficiency of some existing techniques. In particular, likelihood based models, robustness, denoising correlated data and additive modeling are proposed for investigation. Finally, some statistical inference problems arising from processing curves and images data are investigated.