**Statistics Seminar****（****2017-21****）**

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**Topic****:** Non- and semi-parametric Object-oriented Data Analysis for random density functions

**Speaker:** Andreas Kryger Jensen, University of Copenhagen

**Time: **Thursday, December 14, 15:15-16:15

**Place: **Room 217, Guanghua Building 2

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**Abstract:**

The topic of Functional Data Analysis (FDA) has played a noticeable role in the development of contemporary statistical methodology during the last 10 to 15 years. A primary focus of FDA has been on extending existing multivariate statistical methods to settings where either the outcome or an explanatory variable belongs to a linear function space. A natural extension is to pursue similar methodological developments for non-linear function spaces. An assortment of such extensions has more recently been given the name Object-oriented Data Analysis (ODA). In the functional version of ODA the aim is to model infinite dimensional random objects belonging to some non-linear manifold.

In this talk I will present both a non-parametric and a semi-parametric regression model where the functional objects are random density functions. These are continuous and strictly positive functions integrating to one on a compact domain thus belonging to a convex Banach-manifold. The motivation for considering these models is a medical application with the purpose of predicting and discriminating between different severities of heart failure in human patients based on CT scanning measurements of the density of lung tissue.

In the semi-parametric model the density functions are the outcomes, and we consider an ANOVA-type model, where the variability between heart failure severities is decomposed into a parametric and a non-parametric component. The parametric component of this model is given by a set of interpretable parameters representing characteristics such as location, scale and shape, while the residuals are non-parametric boundary-preserving diffeomorphisms. I will show how this model can be estimated by a combination of non-linear least squares and a non-parametric version of the Fisher-Rao metric through a convenient isometry.

**Introduction:**

Andreas Kryger Jensen obtained his MSc in 2010 and in 2014 his PhD degree in Biostatistics from the University of Southern Denmark. The topic of his PhD was methods for classifying marked point process observations. From 2014 he has been employed at the Section of Biostatistics at the University of Copenhagen; first as a Postdoc and from 2015 as Assistant Professor. His current research interests include statistical modelling of random variables in non-standard spaces. A special focus is on functional data analysis and its applications in bio- and medical statistics.

**Your participation is warmly welcomed!**