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Densidades, regresión y clasificación para datos funcionales

Pamela Nerina Llop Ricardo Fraiman Pablo Ferrari Pedro Morín Víctor Yohaí Liliana Forzani

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Resumen/Descripción – provisto por el repositorio digital
The goal of this tesis is to obtain statistical tools for the analysis of infinite dimensional data. In particular, we are interested in study results of consistency of regression and density estimators for curves and surfaces. In this sense, for a single sample path observed continuously over an interval, Labrador (2008) defined an nonparametric marginal density estimator as an extension of the k-nearest neighbor to the continuous context. Based in this work, the first problem we address in this thesis is to estimate the marginal density of a stationary stochastic process by a i.i.d. sample observated over a fixed interval. In this case, we prove the consistency of the estimator, we find rates of convergence puntual, uniform and we prove its asymptotic normal distribution. Then, we extend the definition of this estimator to one particular class of nonstationary processes obtaining in this case rates of convergence and, as an application of this method, we present a new classification rule for funactional data. In a second stage of this thesis, we study the extension of that estimator to stationaries and nonstationaries ramdom fields and, from dependent sequences, we find explicit rates of convergence for both cases. Finally, based on the universal consistency result for d-dimensional data introduced by Stone (1977), we porove a consistency result for regression estimators in the infinite dimensional context and we use it to prove the consistency of known estimators in separable metric spaces.
Palabras clave – provistas por el repositorio digital

Density function; Regression function; Classification; Functional data; Función de densidad; Regresión; Clasificación; Datos funcionales

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No requiere 2011 Biblioteca Virtual de la Universidad Nacional del Litoral (SNRD) acceso abierto

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Tipo de recurso:

tesis

Idiomas de la publicación

  • español castellano

País de edición

Argentina

Fecha de publicación