Comparison of Positivity in Two EpidemicWaves of COVID-19 in Colombia with FDA

We use the functional data methodology to examine whether there are significant differences between two waves of contagion by COVID-19 in Colombia between 7 July 2020 and 20 July 2021. A pointwise functional t-test is initially used, then an alternative statistical test proposal for paired samples is presented, which has a theoretical distribution and performs well in small samples. Our statistical test generates a scalar p-value, which provides a global idea about the significance of the positivity curves, complementing the existing punctual tests, as an advantage.Government of Andalusia (Spain) PID2020-113961GB-I00Ministry of Science and Innovation, Spain (MICINN) Spanish GovernmentEuropean Commission CEX2020-001105-M/AEI/10.13039/501100011033.Junta de Andaluci

Scalar Variance and Scalar Correlation 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.Government of Andalucia (Spain) FQM-307Junta de Andalucia A-FQM-66-UGR20European Commissio

Acerca de la estimación de la fracción PM2.5/PM10

Se discute la estimación de la fracción PM2.5/PM10, que algunos autores reportan como la razón PM2.5/PM10. Estudios previos destacan la importancia de esta fracción en el estudio del impacto de las partículas en el aire sobre la salud de las personas y su uso potencial en la reconstrucción y en la imputación de datos de los niveles de partículas finas PM2.5 a partir de los niveles de partículas gruesas PM10. Se sugiere adaptar la estimación, mediante el uso de diferentes estrategias para situaciones particulares, incluyendo el modelo lineal general (GLM), la regresión a través del origen (RTO), los modelos aditivos generalizados (GAM) y los modelos de regresión usando mínimos cuadrados ponderados (WLS)