Scalar Variance and Scalar Correlation for Functional Data

In Functional Data Analysis (FDA), the existing summary statistics so far are elements in Hilbert space L2 of square-integrable functions. These do not constitute an ordered set; therefore, they sufficient to solve problems related comparability such as obtaining a correlation measurement or comparing variability between two sets curves, determining efficiency and consistency functional estimator, among other things. Consequently, we present approach coherent redefinition some common sample variance, covariance (FDA). Regarding data, our lead numbers instead functions which is helpful for solving aforementioned problems. Furthermore, briefly discuss forms coherence already FDA. We formally enumerate demonstrate properties statistics. Then, simulation study presented briefly, with evidence proposed variance. Finally, implementation through application examples.