Heterogeneous Spatial Dynamical Regression in a Hilbert-Valued Context |
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| Authors: | M D Ruiz-Medina V V Anh R M Espejo M P Frías |
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| Institution: | 1. Department of Statistics and Operation Research, Faculty of Sciences , University of Granada , Spain mruiz@ugr.es;3. School of Mathematical Sciences , Queensland University of Technology , Brisbane , Australia;4. Department of Statistics and Operation Research, Faculty of Sciences , University of Granada , Spain;5. Department of Statistics and Operation Reseach, Sciences and Health Faculty , University of Jaén , Jaén , Spain |
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| Abstract: | This article introduces a Hilbert-valued spatially dynamic regression model. The spatially heterogeneous functional trend is modeled by functional multiple regression, with varying regression operators. The spatial autoregressive Hilbertian model of order one (SARH(1) model, see 37
Ruiz-Medina , M.D. 2011 . Spatial autoregressive and moving average Hilbertian processes . J. Multivariate Anal. 102 : 292 – 305 .Crossref] , Google Scholar]]) is considered to represent the spatial correlation and dynamics displayed by the functional error term. The RKHS theory is applied in the construction of suitable bases for projection and regularization of the associated estimation problems. The performance of the proposed Hilbert-valued modeling and estimation methodology is illustrated with a real-data example, related to financing decisions from firm panel data. |
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| Keywords: | Capital structure of firms Financial functional data Heterogeneous spatial regression Hilbert-Schmidt regression operators Hilbert-valued two-parameter martingale difference sequences Spatial autoregressive Hilbertian processes |
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