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Brief Review of Functional Data Analysis: A Case Study on Regional Demographic and Economic Data

Abstract:

Functional data analysis (FDA) is an important recent field in statistics that enables us to analyze data with dependency over continuous frames and has many applications in various scientific areas. In Ecuador, there is not much use of these methods, and even less in the analysis of demographic and economic variables. In the present study, we firstly describe the general techniques used in FDA and some relevant studies performed with data from Ecuador. Then, we carry out an exploratory analysis with FPCA, functional clustering and PCA on data sets considering fertility, infant mortality, life expectancy, MPI, HDI and GDP growth indexes as variables. Observations for twenty Latin American countries during time frames around 1960–2018 were obtained. We found evidence for homogeneous behavior of variance among life expectancy, MPI and HDI. GDP growth rates reported to have a different functional nature. Haiti, Honduras and Venezuela were determined to have outlying observations for some variables. Our conclusions emphasize the advantages of using FDA techniques in comparison to classical multivariate methods for creating holistic approaches in data analysis.