Scalar Variance and Scalar Correlation for Functional Data Urbano León, Cristhian Leonardo Escabias Machuca, Manuel Ovalle Muñoz, Diana Paola Olaya Ochoa, Javier Correlation for functional data Covariance for functional data FDA Summary statistics in functional data; Variance for functional data In Functional Data Analysis (FDA), the existing summary statistics so far are elements in the Hilbert space L2 of square-integrable functions. These elements do not constitute an ordered set; therefore, they are not sufficient to solve problems related to comparability such as obtaining a correlation measurement or comparing the variability between two sets of curves, determining the efficiency and consistency of a functional estimator, among other things. Consequently, we present an approach of coherent redefinition of some common summary statistics such as sample variance, sample covariance and correlation in Functional Data Analysis (FDA). Regarding variance, covariance and correlation between functional data, our summary statistics lead to numbers instead of functions which is helpful for solving the aforementioned problems. Furthermore, we briefly discuss the functional forms coherence of some statistics already present in the FDA. We formally enumerate and demonstrate some properties of our functional summary statistics. Then, a simulation study is presented briefly, with evidence of the consistency of the proposed variance. Finally, we present the implementation of our statistics through two application examples. 2023-05-24T07:18:08Z 2023-05-24T07:18:08Z 2023-03-09 journal article Urbano-Leon, C.L.; Escabias, M.; Ovalle-Muñoz, D.P.; Olaya-Ochoa J. Scalar Variance and Scalar Correlation for Functional Data. Mathematics 2023, 11, 1317. https://doi.org/10.3390/math11061317 https://hdl.handle.net/10481/81771 10.3390/math11061317 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional MDPI