A Comprehensive Framework for Fully Efficient Robust Estimation and Variable Selection, with Application to High-Dimensional and Complex Data

这项研究解决了在当今复杂的数据结构的背景下，在估计和变量选择的鲁棒性。研究的首要主题是，仔细指定的时刻限制与适当的加权数据相结合，将导致估计和变量选择的充分效率的理想目标，在非典型观测的存在下保持稳定。该方法是通过广义经验似然法开发的，它为每个观察产生估计的权重。在此过程中，这会自动降低可能偏离模型的观测值的权重，从而降低它们的影响。同时，如果模型被正确地指定，即使在有限样本下，与完全有效的基于模型的估计相比，估计的效率也没有损失。采取这种观点允许一个统一的框架，以建设强大的和有效的程序，可以开发各种型号。效率和鲁棒性的基础允许变量选择被构建到方法中来处理，不仅是适度的，而且是高维的设置。由于基线方法的性能，在污染和错误指定下的变量选择一致性可以改善现有的选择方法，这些方法可能已经不稳健或不完全有效。现代科学数据的特点是信息丰富。数据爆炸已经出现在从药物发现到金融市场甚至国土安全的各个领域。虽然大量数据的涌入导致了这些领域的突破，但它也带来了许多统计问题。特别是，它可以是一个压倒性的任务，以确定相关的预测变量，提供一个合适的模型。与此同时，在今天复杂的数据下，这种假设模型肯定只是对现实的简化。因此，不可避免的是，一些数据将偏离，也许是显着的，从模型，虽然它仍然是有用的大部分数据，并可以提供有意义的见解。这项研究的目标是开发技术来进行估计和变量选择的基本任务，同时也允许一些数据偏离模型，而不会对结果产生很大影响。从这项研究中开发的方法是强大的离群值和模型误设，同时仍然保持效率的估计和变量选择，即使在这种污染的存在。因此，它将是在面对复杂数据时取得有意义结果的一个关键组成部分。

This research addresses robustness in both estimation and variable selection within the context of today's complex data structures. The overarching theme of the research is that carefully specified moment restrictions combined with appropriate weighting of the data will lead to the ideal goals of full efficiency in estimation and variable selection which remains stable in the presence of atypical observations. The methodology is developed via generalized empirical likelihood, which yields estimated weights for each observation. In the process, this automatically downweights observations that may deviate from the model, thus reducing their influence. Meanwhile, the estimators have no loss of efficiency compared with the fully efficient model-based estimator if the model were correctly specified, even in finite samples. Taking this point of view allows a unified framework to the construction of robust and efficient procedures that can be developed for a variety of models. The foundation of efficiency and robustness allows variable selection to be built into the methods to handle, not only the moderate, but also the high-dimensional setting. Due to the performance of the baseline approach, the variable selection consistency under contamination and misspecification can improve on existing selection methods that rest on a starting point that may be already non-robust or less than fully efficient. Modern scientific data is characterized by a wealth of information. The data explosion has arisen in diverse areas running the gamut from drug discovery to the financial markets and even homeland security. While the massive influx of data has led to breakthroughs in these fields, it brings many statistical issues to the forefront. In particular, it can be an overwhelming task to determine the relevant predictor variables that provide a suitable model. Meanwhile, with today's complex data, this postulated model will surely be only a simplification of reality. Thus it is inevitable that some of the data will deviate, perhaps significantly, from the model, although it is still useful for the bulk of the data and can provide meaningful insight. This research targets the essential task of developing techniques to perform estimation and variable selection, while also allowing for some of the data to deviate from the model without greatly affecting the results. The methods developed from this research are robust to outliers and model misspecification, while still maintaining efficiency for both estimation and variable selection even in the presence of this contamination. Thus it will be a key component to enable meaningful results in the face of complex data.