Semiparametic Efficient Inference Methods in Complex Data Models

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Nowadays more and more massive and high-dimensional data become available in many scientific fields such as medical and health science, astronomy and physics, computer science and engineering, as well as economics and finance. A challenging task in high-dimensional data analysis is how to select the most relevant predictors among a large number of candidate variables to accurately predict a response variable of interest. High-dimensional variable selection problem has drawn a lot of attention in statistics, as well as in computer science and engineering. However, most research has been focusing on linear models where all variables are assumed to be precisely measured. On the other hand, real data applications always involve nonlinear relationships and variables that are either not directly observable or imprecisely measured. Therefore it is of theoretical and practical interests to study the high-dimensional variable selection problem in measurement error models. One possible direction of investigation is novel regularization methods that incorporate instrumental variables. Moreover, nonlinear relationships will be investigated because they arise in many fields including compressive sensing, signal processing and imaging. ***Survival and event history data analysis arises in many scientific disciplines including medical and health science, engineering, business and economics. However, the main stream methods rely on certain parametric or semiparametric models that have limited flexibility to model real life data. An alternative approach is based on an underlying stochastic process which, for example, represents an individual's health status. The event of interest occurs when this random process reaches a certain threshold for the first time. The first passage time has applications in many other disciplines including biology, chemistry, epidemiology, finance, and physics. However, the computation of the first passage time distributions is a challenging task. The proposed research will develop novel methods for calculation of the first passage time distributions. The new tools will provide much more flexible and general models for survival and event history data analysis.***The proposed research will provide opportunities for the training of highly qualified personnel at all levels. They will be trained to be the experts in the areas that are currently very active and in the research fronts in statistics. Moreover, they will learn modern statistical theories and methodologies, and computational skills to deal with large scale and high-dimensional data. They will also learn to apply these methodologies and skills to solve real life problems.**