Modern Functional Statistical Analysis: Application to Air Pollutant in London Marylebone Road

Abstract

Air pollution in developed countries has a significant impact on people’s lives. It has arisen and manifested itself by the high levels of smoke produced by industries or traffic, forcing authorities to search mechanisms to better control air quality in real-time. Notably, the air pollution levels in London exceed legal and World Health Organisation limits. For example, in 2010, air pollution caused a range of health problems in the capital and representing an economic cost of up to £3.7 billion. In this paper, we consider the daily curve of the concentration of the previous gases collected by the Marylebone road monitoring site in London (contains the hourly measurements taken during the two years 2017 and 2018 for the following four variables: Ozone (O3), Nitric Oxides (NO), Nitrogen Dioxide (NO2), and Sulphur Dioxide (SO2)). Our main objective is to look for the best forecast models for air pollutant concentration. For this purpose, we develop a new procedure to analyze palling gas data in real-time. More precisely, we use the recent mathematical statistics tools to investigate the relationship between the palling gases such as ozone, nitric oxides, nitrogen dioxide, and sulphur dioxide. Specifically, we use functional models like classical functional regression, robust functional regression, and functional relative error regression with kernel and local linear approaches to predict the maximum concentration of air pollutant gases quantities. We show that our prediction approaches’ accuracy is closely linked to the choice of the regression model and the input variables (or the covariates). In particular, the data analysis shows the efficiency and superiority of the nonparametric regression model compared to the other models when the regressors are NO2 and SO2.