Program

Data analysis using regression methods deals with mean, normal, weighted, truncated, etc. in conditional terms. We are changing approaches to strengthen the properties of the estimation, in particular the robustness of the estimators. We develop the moments of the estimated distribution to describe the analysed data set as efficiently as possible. We carry out clustering, classification, in order to obtain information that can inform further analysis or decision-making.

Regressions referred to conditional means can be written and applied to all possible known versions of multivariate models. The estimators are known and well defined, described in the literature. Regressions relating to conditional quantiles add a new aspect to the analyses. It enables a different description of the analysed data by adding the quantile order, being used in a regression approach.

In this talk on applications of quantile regression in data classification, we will discuss some selected approaches in data analysis, including those for time series underlying investment decisions and spatially for demographic and social data.

Robust estimation is a necessary preliminary step of outlier detection. Both involve the specification of slightly arbitrary tuning parameters, like the trimming level, the efficiency or the breakdown point, significance levels or thresholds for outlier tests.
I will first introduce a version of the Forward Search which can be used for adaptive robust estimation, regression, and clustering.
I will then discuss how one can use information criteria for outlier identification, regardless of the chosen method for robust estimation.
All procedures presented are free from the choice of any tuning parameter. Theoretical results will show under what circumstances the procedures
have the desirable properties. Illustrations will be based on data sets from different fields.
This talk is based on joint works with Anthony Atkinson, Andrea Cerioli, Aldo Corbellini, Fabrizio Laurini, and Marco Riani.

Modern prediction algorithms such as random forests and deep learning use training data to construct rules for the prediction of future cases. In any given application we would like to answer the question "how accurate are the rule's predictions?"
Resampling methods have played a central role in the answers: cross-validation, bootstrap estimates, covariance penalties (Mallows' Cp and Akaike's Information Criterion), and, most recently, conformal inference. This talk is intended as an overview, comparing and contrasting the methods, as well as discussing their advantages and disadvantages. Technical issues will be kept to a minimum, and no prior familiarity of prediction algorithms is assumed.