A review on specification tests for models with functional data
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Abstract
Nowadays, due to the progress in technological advances, massive amounts of data are generated. As a result, new statistical methodology is needed to properly manage this information.
The functional data are an example of special importance. These are mainly obtained by means of high-frequency measurements (spectrometric curves, stock prices recording, etc.). Since the beginning of this century, this type of data has achieved great popularity. This fact has generated new distribution or regression models, among others, appropriate to the functional context. In the last 10 years, novel specification tests are proposed for those models. These are generalizations of methodologies developed for the vectorial framework over the last century. Besides, innovative procedures based on distance correlation ideas have been proposed as well. This article reviews the most notable developments in this context, providing some illustrations from real data sets.
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González Manteiga, W. (2023). A review on specification tests for models with functional data. Spanish journal of statistics, 4, 9-40
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This paper is a consequence of the invitation from Editor of this journal and the President of the Instituto Nacional de Estadística (INE) to produce an article as the second recipient of the Premio Nacional de Estadística. I am really grateful to both of them. The creation of the Spanish National Prize in Statistics was an excellent initiative of professor Juan Manuel Rodríguez Poo (the before mentioned president). This represents a fantastic link between the INE and the developments of Statistics in Spain. This work would not have been possible without the collaboration of all my co-authors: Rosa María Crujeiras Casais, Manuel Febrero Bande, Laura Freijeiro González, Eduardo García Portugués y Alejandra María. López Pérez. My acknowledgment also extends to the rest of my co-authors and all my past students in my academic life. I am an researcher interested in
Statistics as a consequence of all I have learned from them.
The research of Wenceslao González-Manteiga is supported by Project PID2020-116587GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” and the Competitive Reference Groups 2021 – 2024 (ED431C 2021/24) from the Xunta de Galicia through the ERDF. Besides, I acknowledge the computational resources from the Supercomputing Centre of Galicia (CESGA).
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional