Describing the concentration of income populations by functional principal component analysis on Lorenz curves

Bongiorno, Enea G.; Goia, Aldo

doi:10.1016/j.jmva.2018.09.005

Cited by 17 publications

(5 citation statements)

References 21 publications

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“…The need of developing novel methodological frameworks able to correctly characterize the data through the use of non‐standard geometries is nowadays becoming widely recognized in FDA, not only for density data but also for other kinds of constrained functional data (see, e.g. Bongiorno & Goia, ; Canale & Vantini, ; Rossini & Canale, ).…”

Section: Introductionmentioning

confidence: 99%

Weighting the domain of probability densities in functional data analysis

Talská

Menafoglio

Hron

et al. 2020

Stat

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In functional data analysis, some regions of the domain of the functions can be of more interest than others owing to the quality of measurement, relative scale of the domain, or simply some external reason (e.g. interest of stakeholders). Weighting the domain is of interest particularly with probability density functions (PDFs), as derived from distributional data, which often aggregate measurements of different quality or are affected by scale effects. A weighting scheme can be embedded into the underlying sample space of a PDF when it is considered as continuous compositions applying the theory of Bayes spaces. The origin of a Bayes space is determined by a given reference measure, and this can be easily changed through the well‐known chain rule. This work provides a formal framework for defining weights through a reference measure, and it is used to develop a weighting scheme on the bounded domain of distributional data. The impact on statistical analysis is illustrated through an application to functional principal component analysis of income distribution data. Moreover, a novel centred log‐ratio transformation is proposed to map a weighted Bayes space into an unweighted space, enabling to use most tools developed in functional data analysis (e.g. clustering and regression analysis) while accounting for the weighting scheme. The potential of our proposal is shown on a real case study using Italian income data.

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Section: Introductionmentioning

confidence: 99%

Weighting the domain of probability densities in functional data analysis

Talská

Menafoglio

Hron

et al. 2020

Stat

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“…However, this idea was also developed for samples of distribution functions [94], samples of level sets [41], etc. In this Special Issue, Bongiorno and Goia [24] revisit the theory of FPCA for dealing with samples of Lorenz curves. These curves are of interest in econometrics but some of their characteristics pose mathematical challenges, e.g., in connection with the construction of a suitable vector space structure.…”

Section: Analysis Of Estimated Functional Datamentioning

confidence: 99%

Recent advances in functional data analysis and high-dimensional statistics

Aneiros

Cao

Fraiman

et al. 2019

Journal of Multivariate Analysis

124

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“…FDA supports reducing the dimensionality of the data and using supplementary critical sources of pattern and variation 1 without the demand of restrictive hypotheses 7 . For these reasons, recently, we are witnessing an uninterrupted growth of methodological research on FDA that attempts to replicate, in a functional key, a large part of classical statistics 1,2,8‐10 . In addition, there is a constant development of novel applications and suggestions to answer particular dilemmas in singular contexts employing functional instruments 11‐16 …”

Section: Introductionmentioning

confidence: 99%

“…7 For these reasons, recently, we are witnessing an uninterrupted growth of methodological research on FDA that attempts to replicate, in a functional key, a large part of classical statistics. 1,2,[8][9][10] In addition, there is a constant development of novel applications and suggestions to answer particular dilemmas in singular contexts employing functional instruments. [11][12][13][14][15][16] Because FDA is widely appreciated as a valuable tool for analyzing biomedical data, research on curves' supervised classification is lively.…”

Section: Introductionmentioning

confidence: 99%

Pooling random forest and functional data analysis for biomedical signals supervised classification: Theory and application to electrocardiogram data

Maturo

Verde

2022

Statistics in Medicine

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Scientific progress has contributed to creating many devices to gather vast amounts of biomedical data over time. The goal of these devices is generally to monitor people's health conditions, diagnose, and prevent patients' diseases, for example, to discover cardiovascular disorders or predict epileptic seizures. A common way of investigating these data is classification, but these instruments generate signals often characterized by high dimensionality. Learning from these data is definitely a challenging task due to many issues, for example, the trade‐off between complexity and accuracy and the course of dimensionality. This study proposes a supervised classification method based on the joint use of functional data analysis, classification trees, and random forest to deal with massive biomedical data recorded over time. For this purpose, this research suggests different original tools to extract features and train functional classifiers, interpret the classification rules, assess leaves' quality and composition, avoid the classical drawbacks due to the COD, and improve the accuracy of the functional classifiers. Focusing on ECG data as a possible example, the final purpose of this study is to offer an original approach to identify and classify patients at risk using different types of biomedical signals. The results confirm that this line of research is exciting; indeed, the interpretative tools show evidence to be very useful for understanding classification rules. Furthermore, the performance of the proposed functional classifier, in terms of accuracy, is excellent because the latter breaks the previous classification record regarding a well‐known ECG dataset.

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Describing the concentration of income populations by functional principal component analysis on Lorenz curves

Cited by 17 publications

References 21 publications

Weighting the domain of probability densities in functional data analysis

Weighting the domain of probability densities in functional data analysis

Recent advances in functional data analysis and high-dimensional statistics

Pooling random forest and functional data analysis for biomedical signals supervised classification: Theory and application to electrocardiogram data

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