PhD Defense Maria Laura Battagliolas

Title: Quantile regression for scalar and functional clustered data and data analysis with phase-amplitude separation

In this thesis we present results arising from either quantile regression, functional data analysis or a combination of the two fields.

First of all, we study quantile regression for clustered data in the cases when the number of clusters is much larger than the observations per cluster. Via simulation studies we demonstrate that some classical estimators for the population-level quantile regression parameters exhibit bias when considering heteroskedastic models at quantile levels different from the median. We propose an estimator whose bias adjustment is based on bootstrap, which we also rely on in order to build confidence intervals. We apply the new estimation methods to data arising from a clinical study concerning AIDS.

We analyze the aforementioned framework further when functional covariates are introduced and data has a longitudinal structure. In particular, we establish the modelling setting, we propose an estimation method for the approximation of the functional coefficient, and we clearly outline how to implement estimation relying on existing software. Our work is motivated by an application in animal science, in which we study the impact of temperature, considered as functional, on low quantiles of feed intake of lactating sows, whose daily conditions were recorded several times over the lactating days, which we take as longitudinal time points.

Our last contribution concerns functional data analysis and revolves around the analysis of learning curves of mice undergoing memory-involving tasks repeatedly. We rely on existing methods that study bivariate functional objects constituted by amplitude and phase components arising from the registration of a collection of curves. The multivariate functional principal component analysis of such objects gives us an insight on the differences and similarities of the learning behaviors of two groups of mice, one where the animals were induced with a brain lesion similar to that observed in patients affected by psychiatric disorders such as schizophrenia, and a control group.

Link to thesis

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Supervisor: Prof. Helle Sørensen, University of Copenhagen
Co-supervisor: Prof. Anders Tolver, University of Copenhagen
Co-supervisor: Prof. Ana-Maria Staicu, North Carolina State University

Assessment committee:

Prof. Marco Geraci, Sapienza,  University of Rome
Associate Prof. Lina Schelin, Umeå University
Associate Prof. Bo Markussen (chairman), University of Copenhagen