DMS Statistics and Data Science Seminar

Speaker: Marco Riani (Professor of Statistics, University of Parma, Italy)

Title: Robust and efficient regression analysis with applications

Abstract: Data rarely follow the simple models of mathematical statistics. Often, there will be distinct subsets of observations so that more than one model may be appropriate. Further, parameters may gradually change over time. In addition, there are often dispersed or grouped outliers which, in the context of international trade data, may correspond to fraudulent behavior. All these issues are present in the datasets that are analyzed on a daily basis, for example, by the Joint Research Centre of the European Commission and can only be tackled by using methods which are robust to deviations to model assumptions. In this talk, we suggest a system of interrogating robust analyses, which we call “monitoring” and describe a series of robust and efficient methods to detect model deviations, groups of homogeneous observations multiple outliers and/or sudden level shifts in time series. Particular attention will be given to robust and efficient methods (known as forward search) which enables to use a flexible level of trimming and understand the effect that each unit (outlier or not) exerts on the model. Finally we discuss the extension of the above methods to transformations and to the big data context. The Box-Cox power transformation family for non-negative responses in linear models has a long and interesting history in both statistical practice and theory. The Yeo-Johnson transformation extends the family to observations that can be positive or negative. In this talk we describe an extended Yeo-Johnson transformation that allows positive and negative responses to have different power transformations.