A hacking day of Mathematics for Data Science at the Department of Mathematics

# Alicia Nieto Reyes

(Departamento de Matemáticas, Estadística y Computación, Univesidad de Cantambria
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Bio Alicia Nieto Reyes is Profesor Contratado Doctor´´ at the Department of Mathematics, Statistics and Computer Science of the University of Cantabria, Spain; where she has been since June 2006. Her main research area is in multivariate and functional data analysis. She specializes in particular on statistical depth functions.

## Syllabus

It is well know in multivariate analysis that the coordinate-wise median is not an adequate measure of centrality. To order a data set in the real numbers, it is reasonable to follow the decreasing order of the absolute values of the difference between the percentiles of the points in the set and the percentile 50. Thus, the data set central points are the median(s) of the dataset. In contraposition, the component-wise median of a sample is not necessarily similar to any element of the sample and may fall outside the convex-hull of the data. This is because, if our data set is in a dimension higher than one, the median has to be calculated coordinate by coordinate. Tukey introduced the notion of statistical depth as a way to emulate the behavior of the one-dimensional quantiles, and median, to give a concept of order valid for spaces whose dimension is higher than one. Informally, the data is ordered such that, if a datum is moved toward the center of the data cloud, its depth increases, and, if it is moved toward the outside, its depth decreases. Thus, finding the deepest point in a set is the same as finding the point that is most inside the points cloud or, roughly speaking, the one with most points around it. In these seminars we will introduce the concept of depth for multivariate and functional spaces.

## References

• Zuo, Yijun; Serfling, Robert. General notions of statistical depth function. Ann. Statist. 28 (2000), no. 2, 461–482. doi:10.1214/aos/1016218226.

• Nieto-Reyes, Alicia; Battey, Heather. A Topologically Valid Definition of Depth for Functional Data. Statist. Sci. 31 (2016), no. 1, 61–79. doi:10.1214/15-STS532.

## Schedule

• 6 September 2019, 09:30-11:00 @ Povo 1, Room A221
• 6 September 2019, 11:15-12:45 @ Povo 1, Room A221
• Poster: PDF

## Details

• The participation is free. Please send an email to Prof. Claudio Agostinelli.