Robust Inference

一般来说，估计面临两个不确定性来源：抽样变异性和污染偏差。在过去的一个世纪里，抽样变异性的研究一直是统计理论和实践的主要焦点。另一方面，由于数据质量差/不均匀、数据污染、数据缺失、严重误差等导致的偏差却很少受到关注。与抽样变异性不同，污染偏差很难建模和测量，并且不会随着样本量的增加而减少。对于中等和大型数据集，由数据质量（污染偏差）引起的不确定性通常大于由抽样可变性引起的不确定性。目前的稳健性理论主要关注数据质量问题，并至少部分解决了数据污染偏差问题。在接下来的几年里，我将继续在以下主题进行研究：(a)线性模型的稳健变量选择，分类和聚类分析(b)估计线性模型估计的污染偏差界限(c)开发稳健方法(线性回归，散点估计，等)在一般污染模型（包括单元格污染和案例污染）下是稳健的，并且可以应用于非常大的数据集(d)开发新模型来表示高度多变量环境中的数据污染(e)使稳健估计适应涉及缺失数据的情况(f)评估缺失数据在稳健估计中的影响。拟议的研究具有理论相关性，也有可能在包括数据挖掘和生物信息学在内的许多领域增强强大方法的有用性和适用性。

In general, estimates face two sources of uncertainty: sampling variability and contamination bias. The study of sampling variability has constituted the main focus of statistical theory and practice in the past century. On the other hand, the bias caused by poor/uneven data quality, data contamination, missing data, gross errors, etc. has received much less attention. Unlike sampling variability, contamination bias is difficult to model and measure and does not diminish with increasing sample sizes. For moderate and large data sets, the uncertainty due to data quality (contamination bias) usually dominates the uncertainty due to sampling variability. The current robustness theory is mainly concerned with issues of data quality and addresses, at least in part, the problem of data contamination bias. In the next few years I will continue to conduct research in the following topics (a) Robust variable selection for linear models, classification and cluster analysis (b) Estimation of contamination bias bounds for linear model estimates (c) Development of robust methods (linear regression, scatter estimates, etc.) that are robust under general contamination models (including cellwise and casewise contamination) and can be applied to very large datasets (d) Development of new models to represent data contamination in highly multivariate settings (e) adapting robust estimates to situations involving missing data (f) assessing the effect of missing data in robust estimates. The proposed research has theoretical relevance and also the potential to enhance the usefulness and applicability of robust methodology in many fields including data mining and bioinformatics.