Análisis estadístico funcional espacial de datos de panel

Resumen

This thesis opens new research lines in the field of Spatial and/or Temporal Functional Statistics. The original motivation of the thesis was to contribute to the field of panel data analysis adopting a functional perspective. Specifically, the primary objective of this thesis was to derive flexible statistical models and methodologies for the analysis of correlated curve data in space, or alternatively, for correlated surfaces in time, covering, in particular, the infinite-dimensional multivariate framework. Summarizing, the main contributions of this thesis are related to - The implementation of Spatial Autoregressive Hilbertian predictors by projection. - The formulation of new classes of models in the context of spatial functional multiple regression when response and regressors are Hilbert-valued variables, considering the case where the regression operators are spatially heterogeneous. - The introduction of spatial functional classification Techniques based on the estimation of spatial mixed effect models with fixed and random effect curves having a heterogeneous behavior in space. - The extension of the proposed weak-dependent models in the context of spatial time series theory to the long-range dependence case in terms of Gegenbauer polynomials. - The formulation of new RKHS based penalized estimation methodologies for autoregressive Hilbertian processes. - The derivation of sufficient conditions for the asymptotic normal distribution of maximum likelihood estimators for Gaussian autoregressive Hilbertian processes. - Finally, the consideration of the theory of multifractional pseudodifferential operators for the representation of heterogeneous curve data behaviors in space (i.e., variable order of differentiation in the weak and mean-square senses), solving the associated functional least-squares estimation problem.