Data-Analytic Modeling for High-Dimensional Data

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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.