Functional Cluster and Canonical Correlation Analysis of EU Countries by Number of Daily Deaths and Stringency Index During Covid-19 Pandemic


Abstract


The danger of a global pandemic, such as the new Coronavirus (Covid-19),is obvious. This study aims to investigate the behavior and relationship of thenumber of daily new conrmed deaths per million and the stringency indexof twenty-seven European Union (EU) countries by utilizing functional clusteranalysis and functional canonical correlation analysis. Functional clusteranalysis was used to observe how countries cluster together according to dailydeaths during the time interval between March and July 2020. Functionalcanonical correlation analysis was also utilized to measure the correlationbetween the frequency index and daily deaths, and also to determine therelative positions of countries concerning their respective variability structure.The data is obtained from OWID. Here, it is seen that Italy, Spain,Belgium, and France are particularly aected by the pandemic during thetime interval within the EU countries, and the course of daily deaths is in adierent position compared to other EU countries. At the same time, a veryhigh relationship emerged between the stringency index and daily deaths asexpected.

DOI Code: 10.1285/i20705948v14n1p197

Keywords: Covid 19; pandemic; functional cluster analysis; functional canonical correlation analysis; public health

References


Beltekian, D., Gavrilov, D., Giattino, C., et al. (2020). Data on COVID-19 (coronavirus) by Our World in Data. dataset available at https://github.com/owid/covid-19-data/tree/master/public/data. Accessed 01 July 2020.

Chowdhury, R., Heng, K., Shawon, M. S. R., Goh, G., Okonofua, D., Ochoa-Rosales, C., ... & Shahzad, S. (2020). Dynamic interventions to control COVID-19 pandemic: a multivariate prediction modeling study comparing 16 worldwide countries. European journal of epidemiology, 35(5), 389-399.

Clarkson, D. B., Fraley, C., Gu, C., & Ramsay, J. (2005). S+ Functional Data Analysis: User's Manual for Windows®. Springer Science & Business Media.

Cupidon, J., Gilliam, D. S., Eubank, R., & Ruymgaart, F. (2007). The delta method for analytic functions of random operators with application to functional data. Bernoulli, 13(4), 1179-1194.

Cupidon, J., Eubank, R., Gilliam, D., & Ruymgaart, F. (2008). Some properties of canonical correlations and variates in infinite dimensions. Journal of Multivariate Analysis, 99(6), 1083-1104.

da Silva, J. T., & Tsigaris, P. (2020). Policy determinants of COVID-19 pandemic–induced fatality rates across nations. Public Health, 187, 140-142.

ECDC- European Centre for Disease Prevention and Control Website. https://www.ecdc.europa.eu/en/cases-2019-ncov-eueea. Accessed 01 July 2020.

Eubank, R. L., & Hsing, T. (2008). Canonical correlation for stochastic processes. Stochastic Processes and their Applications, 118(9), 1634-1661.

Ferreira, L., & Hitchcock, D. B. (2009). A comparison of hierarchical methods for clustering functional data. Communications in Statistics-Simulation and Computation, 38(9), 1925-1949.

Giraldo, R., Delicado, P., & Mateu, J. (2012). Hierarchical clustering of spatially correlated functional data. Statistica Neerlandica, 66(4), 403-421.

Górecki, T., Krzyśko, M., Waszak, Ł., & Wołyński, W. (2018). Selected statistical methods of data analysis for multivariate functional data. Statistical Papers, 59(1), 153-182.

Górecki, T., Krzyśko, M., & Wołyński, W. (2020). Independence test and canonical correlation analysis based on the alignment between kernel matrices for multivariate functional data. Artificial Intelligence Review, 53(1), 475-499.

He, G., Müller, H. G., & Wang, J. L. (2000). Extending correlation and regression from multivariate to functional data. Asymptotics in statistics and probability, 301-315.

He, G., Müller, H. G., & Wang, J. L. (2003). Functional canonical analysis for square integrable stochastic processes. Journal of Multivariate Analysis, 85(1), 54-77.

He, G., Müller, H. G., & Wang, J. L. (2004). Methods of canonical analysis for functional data. Journal of Statistical Planning and Inference, 122(1-2), 141-159.

Henderson, B. (2006). Exploring between site differences in water quality trends: a functional data analysis approach. Environmetrics: The official journal of the International Environmetrics Society, 17(1), 65-80.

Hitchcock, D. B., Booth, J. G., & Casella, G. (2007). The effect of pre-smoothing functional data on cluster analysis. Journal of Statistical Computation and Simulation, 77(12), 1043-1055.

Hosseininasab, S. M. E., Faridrohani, M., & Golshan, A. M. (2012). Functional analysis of current and noncurrent balance facilities of Iranian export development bank. Journal of Statistical Theory and Applications, 11(2), 121-142.

Huzurbazar, S., & Humphrey, N. F. (2008). Functional clustering of time series: An insight into length scales in subglacial water flow. Water resources research, 44(11).

Jacques, J., & Preda, C. (2014). Functional data clustering: a survey. Advances in Data Analysis and Classification, 8(3), 231-255.

Keser, I. K. (2014). Comparing two mean humidity curves using functiona t-tests: Turkey Case. Electronic Journal of Applied Statistical Analysis, 7(2), 254-278.

Koymen Keser, I., & Deveci Kocakoç, I. (2015). Smoothed functional canonical correlation analysis of humidity and temperature data. Journal of Applied Statistics, 42(10), 2126-2140.

Krzyśko, M., Waszak, Ł. (2013). Canonical correlation analysis for functional data. Biometrical Letters, 50, 95–105.

Kupresanin, A. M. (2008). Topics in functional canonical correlation and regression (Doctoral dissertation, Arizona State University).

Léger, A. E., & Mazzuco, S. (2020). What can we learn from functional clustering of mortality data? An application to HMD data. arXiv preprint arXiv:2003.05780.

Leurgans, S. E., Moyeed, R. A., & Silverman, B. W. (1993). Canonical correlation analysis when the data are curves. Journal of the Royal Statistical Society: Series B (Methodological), 55(3), 725-740.

Madrigal, P. (2017). fCCAC: functional canonical correlation analysis to evaluate covariance between nucleic acid sequencing datasets. Bioinformatics, 33(5), 746-748.

Matabuena, M., Vidal, J. C., Hayes, P. R., Saavedra-García, M., Trillo, F. H. (2019). Application of Functional Data Analysis for the Prediction of Maximum Heart Rate. IEEE Access, 7, 121841-121852. doi: 10.1109/ACCESS.2019.2938466.

Oxford University Government Response Tracker, Data from: Coronavirus government response tracker, 2020; dataset available at https://www.bsg.ox.ac.uk/research/research-projects/coronavirus-government-response-tracker. Accessed 01 July 2020.

Ramsay, J. O. (1982). When the data are functions. Psychometrika, 47(4), 379-396.

Ramsay, J. O. (2004). Functional data analysis. Encyclopedia of Statistical Sciences, 4.

Ramsay, J. O., & Dalzell, C. J. (1991). Some tools for functional data analysis. Journal of the Royal Statistical Society: Series B (Methodological), 53(3), 539-561.

Ramsay, J. O., Hooker, G., & Graves, S. (2009). Introduction to functional data analysis. In Functional data analysis with R and MATLAB (pp. 1-19). Springer, New York, NY.

Ramsay, J. O., & Silverman, B. W. (1997). Functional Data Analysis Springer-Verlag. New York.

Ramsay, J. O., & Silverman, B. W. (2007). Applied functional data analysis: methods and case studies. Springer.

Shin, H., & Lee, S. (2015). Canonical correlation analysis for irregularly and sparsely observed functional data. Journal of Multivariate Analysis, 134, 1-18.

Strandberg, J. (2013). Cluster analysis for functional data, Master thesis, Umeå University. https://www.diva-portal.org/smash/get/diva2:691473/FULLTEXT01.pdf

Tzeng, S., Hennig, C., Li, Y. F., & Lin, C. J. (2018). Dissimilarity for functional data clustering based on smoothing parameter commutation. Statistical methods in medical research, 27(11), 3492-3504.

Wikipedia. (2020). List of sovereign states in Europe by GDP (PPP) per capita. https://en.wikipedia.org/wiki/List_of_sovereign_states_in_Europe_by_GDP_(PPP)_per_capita. Accessed 01 July 2020.

Worldometer Website. COVID-19 Coronavirus Pandemic. https://www.worldometers.info/coronavirus/. Accessed 01 July 2020.


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