Manifold functional multiple regression model with LRD error term
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914677720612864 |
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| author | Ovalle-Muñoz, Diana P. Ruiz-Medina, M. Dolores |
| author_facet | Ovalle-Muñoz, Diana P. Ruiz-Medina, M. Dolores |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_08569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Manifold functional multiple regression model with LRD error term Ovalle-Muñoz, Diana P. Ruiz-Medina, M. Dolores Statistics Theory 60G10, 60G12, 60G18, 60G20, 60G22 (primary) 60G60 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. |
| title | Manifold functional multiple regression model with LRD error term |
| topic | Statistics Theory 60G10, 60G12, 60G18, 60G20, 60G22 (primary) 60G60 |
| url | https://arxiv.org/abs/2402.08569 |