Semiparametic Efficient Inference Methods in Complex Data Models

在医学与健康科学、天文学与物理学、计算机科学与工程、经济学与金融学等众多科学领域中，越来越多的海量数据和高维数据被广泛地应用。在高维数据分析中，一个具有挑战性的任务是如何从大量的候选变量中选择最相关的预测因子来准确地预测感兴趣的响应变量。高维变量选择问题在统计学、计算机科学和工程领域都引起了广泛的关注。然而，大多数研究都集中在线性模型上，其中所有变量都被假设为精确测量。另一方面，真实的数据应用总是涉及非线性关系和变量，这些变量不是直接可观察的，就是不精确测量的。因此，研究测量误差模型中的高维变量选择问题具有重要的理论和实际意义。一个可能的研究方向是新的正则化方法，将工具变量。此外，非线性关系将被研究，因为它们出现在许多领域，包括压缩传感，信号处理和成像。

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.