Robust Inference

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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.