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.