RT Dissertation/Thesis
T1 Nonparametric inference with directional and linear data
A1 García Portugués, Eduardo
A2 Universidade de Santiago de Compostela. Facultade de Matemáticas. Departamento de Estatística e Investigación Operativa, 
K1 Datos direccionales
K1 Análisis estadístico
AB The term directional data refers to data whose support is a circumference, a sphere or, generally,an hypersphere of arbitrary dimension. This kind of data appears naturally in severalapplied disciplines: proteomics, environmental sciences, biology, astronomy, image analysis ortext mining. The aim of this thesis is to provide new methodological tools for nonparametricinference with directional and linear data (i.e., usual Euclidean data). Nonparametric methodsare obtained for both estimation and testing, for the density and the regression curves, in situationswhere directional random variables are present, that is, directional, directional-linear anddirectional-directional random variables. The main contributions of the thesis are collected insix papers briefly described in what follows.In García-Portugués et al. (2013a) different ways of estimating circular-linear and circularcirculardensities via copulas are explored for an environmental application. A new directionallinearkernel density estimator is introduced in García-Portugués et al. (2013b) together withits basic properties. Three new bandwidth selectors for the kernel density estimator with directionaldata are given in García-Portugués (2013) and compared with the available ones. Thedirectional-linear estimator is used in García-Portugués et al. (2014a) for constructing an independencetest for directional and linear variables that is applied to study the dependencebetween wildfire orientation and size. In García-Portugués et al. (2014b) a central limit theoremfor the integrated squared error of the directional-linear estimator is presented. This result isused to derive the asymptotic distribution of the independence test and of a goodness-of-fit testfor parametric directional-linear and directional-directional densities. Finally, a local linear estimatorwith directional predictor and linear response is given in García-Portugués et al. (2014)jointly with a goodness-of-fit test for parametric regression functions.
YR 2015
FD 2015-01-20
LK http://hdl.handle.net/10347/12055
UL http://hdl.handle.net/10347/12055
LA eng
DS Minerva
RD 22 abr 2026