Manifold functional multiple regression model with LRD error term

2024/02/13 by Diana P. Ovalle-Muñoz, Ovalle-Muñoz, Diana P., M. D. Ruiz‐Medina +1
Computer Science · #Face and Expression Recognition

paper · pdf · doi:10.48550/arxiv.2402.08569

Abstract

This paper considers the problem of manifold functional multiple regression with functional response, time--varying scalar regressors, and functional error term displaying Long Range Dependence (LRD) in time. Specifically, the error term is given by a manifold multifractionally integrated functional time series (see, e.g., Ovalle--Muñoz & Ruiz--Medina, 2024)). The manifold is defined by a connected and compact two--point homogeneous space. The functional regression parameters have support in the manifold. The Generalized Least--Squares (GLS) estimator of the vector functional regression parameter is computed, and its asymptotic properties are analyzed under a totally specified and misspecified model scenario. A multiscale residual correlation analysis in the simulation study undertaken illustrates the empirical distributional properties of the errors at different spherical resolution levels.

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