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

This research was funded by project PID2020-113961GB-I00 of the Spanish Ministry of Science and Innovation (also supported by the FEDER program), project FQM-307 of the Government of Andalusia (Spain) and the PhD grant (FPU18/01779) awarded to Christian Acal. The authors also thank the support of the University of Granada, Spain, under project for young researchers PPJIB2020-01.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 NO2, PM10, PM2.5 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 PM10 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.Spanish Ministry of Science and Innovation - FEDER program PID2020-113961GB-I00Government of Andalusia (Spain) FQM-307University of Granada, Spain PPJIB2020-01- FPU18/0177

Basis expansion approaches for functional analysis of variance with repeated measures

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

Functional repeated measures analysis of variance and its application

This paper is motivated by medical studies in which the same patients with multiple sclerosis are examined at several successive visits and described by fractional anisotropy tract profiles, which can be represented as functions. Since the observations for each patient are dependent random processes, they follow a repeated measures design for functional data. To compare the results for different visits, we thus consider functional repeated measures analysis of variance. For this purpose, a pointwise test statistic is constructed by adapting the classical test statistic for one-way repeated measures analysis of variance to the functional data framework. By integrating and taking the supremum of the pointwise test statistic, we create two global test statistics. Apart from verifying the general null hypothesis on the equality of mean functions corresponding to different objects, we also propose a simple method for post hoc analysis. We illustrate the finite sample properties of permutation and bootstrap testing procedures in an extensive simulation study. Finally, we analyze a motivating real data example in detail

Doctor of Philosophy

dissertationThis dissertation aims to develop the theory and applications of functional time series analysis. Functional data analysis came into prominence in the 1990s when more sophisticated data collection and storage systems became prevalent, and many of the early developments focused on simple random samples of curves. However, a common source of functional data is when long, continuous records are broken into segments of smaller curves. An example of this is geologic and economic data that are presented as hourly or daily curves. In these instances, successive curves may exhibit dependencies which invalidate statistical procedures that assume a simple random sample. The theory of functional time series analysis has grown tremendously in the last decade to provide methodology for such data, and researchers have focused primarily on adapting methods available in finite dimensional time series analysis to the function space setting. As a first problem, we consider an invariance principle for the partial sum process of stationary random functions. This theory is then applied to the problems of testing for stationarity of a functional time series and the one-way functional analysis of variance problem under dependence

Do different models induce changes in mortality indicators? That is a key question for extending the Lee-Carter model.

The parametric model introduced by Lee and Carter in 1992 for modeling mortality rates in the USA was a seminal development in forecasting life expectancies and has been widely used since then. Different extensions of this model, using different hypotheses about the data, constraints on the parameters, and appropriate methods have led to improvements in the model’s fit to historical data and the model’s forecasting of the future. This paper’s main objective is to evaluate if differences between models are reflected in different mortality indicators’ forecasts. To this end, nine sets of indicator predictions were generated by crossing three models and three block-bootstrap samples with each of size fifty. Later the predicted mortality indicators were compared using functional ANOVA. Models and block bootstrap procedures are applied to Spanish mortality data. Results show model, block-bootstrap, and interaction effects for all mortality indicators. Although it was not our main objective, it is essential to point out that the sample effect should not be present since they must be realizations of the same population, and therefore the procedure should lead to samples that do not influence the results. Regarding significant model effect, it follows that, although the addition of terms improves the adjustment of probabilities and translates into an effect on mortality indicators, the model’s predictions must be checked in terms of their probabilities and the mortality indicators of interest

Comparative Analysis of Student Learning: Technical, Methodological and Result Assessing of PISA-OECD and INVALSI-Italian Systems .

PISA is the most extensive international survey promoted by the OECD in the field of education, which measures the skills of fifteen-year-old students from more than 80 participating countries every three years. INVALSI are written tests carried out every year by all Italian students in some key moments of the school cycle, to evaluate the levels of some fundamental skills in Italian, Mathematics and English. Our comparison is made up to 2018, the last year of the PISA-OECD survey, even if INVALSI was carried out for the last edition in 2022. Our analysis focuses attention on the common part of the reference populations, which are the 15-year-old students of the 2nd class of secondary schools of II degree, where both sources give a similar picture of the students

Repeated measures analysis for functional data

Most of the traditional statistical methods are being adapted to the Functional Data Analysis (FDA) context. The repeated measures analysis which deals with the k-sample problem when the data are from the same subjects is investigated. Both the parametric and the nonparametric approaches are considered. Asymptotic, permutation and bootstrap approximations for the statistic distribution are developed. In order to explore the statistical power of the proposed methods in different scenarios, a Monte Carlo simulation study is carried out. The results suggest that the studied methodology can detect small differences between curves even with small sample sizes.Repeated measure Functional data analysis Paired design Bootstrap method