Homogeneity problem for basis expansion of functional data with applications to resistive memories

Faced with novel coronavirus outbreak, the most hard-hit countries adopted a lockdown strategy to contrast the spread of virus. Many studies have already documented that the COVID-19 control actions have resulted in improved air quality locally and around the world. Following these lines of research, we focus on air quality changes in the urban territory of Chieti-Pescara (Central Italy), identified as an area of criticality in terms of air pollution. Concentrations of $$\hbox {NO}_{{2}}$$ NO 2 , $$\hbox {PM}_{{10}}$$ PM 10 , $$\hbox {PM}_{2.5}$$ PM 2.5 and benzene are used to evaluate air pollution changes in this Region. Data were measured by several monitoring stations over two specific periods: from 1st February to 10 th March 2020 (before lockdown period) and from 11st March 2020 to 18 th April 2020 (during lockdown period). The impact of lockdown on air quality is assessed through functional data analysis. Our work makes an important contribution to the analysis of variance for functional data (FANOVA). Specifically, a novel approach based on multivariate functional principal component analysis is introduced to tackle the multivariate FANOVA problem for independent measures, which is reduced to test multivariate homogeneity on the vectors of the most explicative principal components scores. Results of the present study suggest that the level of each pollutant changed during the confinement. Additionally, the differences in the mean functions of all pollutants according to the location and type of monitoring stations (background vs traffic), are ascribable to the $$\hbox {PM}_{{10}}$$ PM 10 and benzene concentrations for pre-lockdown and during-lockdown tenure, respectively. FANOVA has proven to be beneficial to monitoring the evolution of air quality in both periods of time. This can help environmental protection agencies in drawing a more holistic picture of air quality status in the area of interest.

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“…This new methodology can be seen as the extension of the parametric and nonparametric approaches proposed by Aguilera et al. ( 2021 ).…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…The relevance of this research work lies in its contribution to extending the parametric and nonparametric functional homogeneity testing procedures proposed by Aguilera et al. ( 2021 ) for univariate functional data to the multivariate case.…”

Section: Introductionmentioning

confidence: 99%

Functional ANOVA approaches for detecting changes in air pollution during the COVID-19 pandemic

Acal

Aguilera

Sarra

et al. 2021

Stoch Environ Res Risk Assess

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“…The most-studied solutions avoid the need for cross-validation to estimate the penalty parameter by reducing the problem to linear regression on uncorrelated predictor variables. Approaches based on functional PCA [36][37][38][39][40][41] and functional Partial Least Squares (PLS) [42][43][44][45][46][47] were widely studied in the literature in the context of different functional regression models.…”

Section: Multiple Function-on-function Linear Modelmentioning

confidence: 99%

COVID-19 Data Imputation by Multiple Function-on-Function Principal Component Regression

et al. 2021

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The aim of this paper is the imputation of missing data of COVID-19 hospitalized and intensive care curves in several Spanish regions. Taking into account that the curves of cases, deceases and recovered people are completely observed, a function-on-function regression model is proposed to estimate the missing values of the functional responses associated with hospitalized and intensive care curves. The estimation of the functional coefficient model in terms of principal components’ regression with the completely observed data provides a prediction equation for the imputation of the unobserved data for the response. An application with data from the first wave of COVID-19 in Spain is developed after properly homogenizing, registering and smoothing the data in a common interval so that the observed curves become comparable. Finally, Canonical Correlation Analysis is performed on the functional principal components to interpret the relationship between hospital occupancy rate and illness response variables.

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“…More recently, a novel approach based on functional principal component analysis was introduced in Aguilera et al. ( 2021a ). The purpose is to reduce the dimension of the problem and conduct a multivariate ANOVA on the vector of the most explicative principal component scores.…”

Section: Introductionmentioning

confidence: 99%

Basis expansion approaches for functional analysis of variance with repeated measures

Acal

Aguilera

2022

Adv Data Anal Classif

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The methodological contribution in this paper is motivated by biomechanical studies where data characterizing human movement are waveform curves representing joint measures such as flexion angles, velocity, acceleration, and so on. In many cases the aim consists of detecting differences in gait patterns when several independent samples of subjects walk or run under different conditions (repeated measures). Classic kinematic studies often analyse discrete summaries of the sample curves discarding important information and providing biased results. As the sample data are obviously curves, a Functional Data Analysis approach is proposed to solve the problem of testing the equality of the mean curves of a functional variable observed on several independent groups under different treatments or time periods. A novel approach for Functional Analysis of Variance (FANOVA) for repeated measures that takes into account the complete curves is introduced. By assuming a basis expansion for each sample curve, two-way FANOVA problem is reduced to Multivariate ANOVA for the multivariate response of basis coefficients. Then, two different approaches for MANOVA with repeated measures are considered. Besides, an extensive simulation study is developed to check their performance. Finally, two applications with gait data are developed.

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Homogeneity problem for basis expansion of functional data with applications to resistive memories

Cited by 11 publications

References 21 publications

Functional ANOVA approaches for detecting changes in air pollution during the COVID-19 pandemic

Functional ANOVA approaches for detecting changes in air pollution during the COVID-19 pandemic

COVID-19 Data Imputation by Multiple Function-on-Function Principal Component Regression

Basis expansion approaches for functional analysis of variance with repeated measures

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