Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors
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A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic normality and strong consistency is obtained, under suitable conditions. The correlation analysis is based on a componentwise estimator of the residual autocorrelation operator. When the dependence structure of the functional error term is unknown, a plug-in generalized least-squared regression parameter estimator is formulated. Its strong consistency is proved as well. A simulation study is undertaken to illustrate the performance of the presented approach, under different regularity conditions. An application to financial panel data is also considered.
KeywordsARH(1) errors Dynamical functional multiple regression Firm leverage maps Generalized least-squared estimator Kernel regressors
Mathematics Subject Classification60G25 60G60 62J05 62J10
This work has been supported in part by project MTM2015-71839-P of MINECO, Sapin (co-funded with FEDER funds). D. Miranda supported by FINCyT, Innóvate Perú.
- Dautray R, Lions JL (1985) Mathematical analysis and numerical methods for science and technology, vol 3. Spectral theory and applications. Springer, New YorkGoogle Scholar
- Ferraty F, Vieu P (2011) Kernel regression estimation for functional data. In: Ferraty F, Romain Y (eds) The Oxford handbook of functional data analysis. Oxford University Press, Oxford, pp 72–129Google Scholar
- Hsing T, Eubank R (2015) Theoretical foundations of functional data analysis, with an introduction to linear operators. In: Wiley series in probability and statistics. Wiley, ChichesterGoogle Scholar