Functional semiparametric partially linear model with autoregressive errors

Authors:
Sophie Dabo-Niang;Serge Guillas
Affiliations:
Université Charles-De-Gaulle-Lille 3, Lille, France;University College London, London, United Kingdom
Venue:
Journal of Multivariate Analysis
Year:
2010

Citing 5
Cited 1

Time series: theory and methods

Time series: theory and methods
Fixed design regression for time series: asymptotic normality

Journal of Multivariate Analysis
Predicting using Box-Jenkins, nonparametric, and bootstrap techniques

Technometrics
Time Series Analysis and Its Applications (Springer Texts in Statistics)

Time Series Analysis and Its Applications (Springer Texts in Statistics)
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)

Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)

Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density

Computational Statistics & Data Analysis

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Abstract

In this paper, we introduce a functional semiparametric model, where a real-valued random variable is explained by the sum of a unknown linear combination of the components of a multivariate random variable and an unknown transformation of a functional random variable. The errors can be autocorrelated. We focus here on the parametric estimation of the coefficients in the linear combination. First, we use a nonparametric kernel method to remove the effect of the functional explanatory variable. Then, we use generalized least squares approach to obtain an estimator of these coefficients. Under some technical assumptions, we prove consistency and asymptotic normality of our estimator. Finally, we present Monte Carlo simulations that illustrate these characteristics.