The goal of this thesis is to bridge the gap between univariate and multivariate quantiles by extending the study of univariate quantile regression and its generalizations to multivariate responses. The statistical analysis focuses on a multivariate framework where we consider vector-valued quantile functions associated with multivariate distributions, providing inferential procedures and establishing the asymptotic properties of the proposed estimators. We illustrate their applicability in a wide variety of scientific settings, including time series, longitudinal and clustered data. The dissertation is divided into four chapters, each of them focusing on various aspects of multivariate analysis and different data types and structures. The methodologies we propose are supported by theoretical results and illustrated using simulation studies and real-world data.

On quantile regression models for multivariate data

MERLO, LUCA
2022

Abstract

The goal of this thesis is to bridge the gap between univariate and multivariate quantiles by extending the study of univariate quantile regression and its generalizations to multivariate responses. The statistical analysis focuses on a multivariate framework where we consider vector-valued quantile functions associated with multivariate distributions, providing inferential procedures and establishing the asymptotic properties of the proposed estimators. We illustrate their applicability in a wide variety of scientific settings, including time series, longitudinal and clustered data. The dissertation is divided into four chapters, each of them focusing on various aspects of multivariate analysis and different data types and structures. The methodologies we propose are supported by theoretical results and illustrated using simulation studies and real-world data.
22-feb-2022
Inglese
Dependent data; M-estimation; multivariate quantiles; quantile regression
PETRELLA, Lea
ALFO', Marco
Università degli Studi di Roma "La Sapienza"
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14242/179003
Il codice NBN di questa tesi è URN:NBN:IT:UNIROMA1-179003