Statistique de la pollution de l'air : méthode mathématiques : applications au cas de la région parisienne
Thèses d'Orsay, no. 538 (1999) , 238 p.

As it occurs in all great cities, Paris has a serious photochemical ozone air pollution problem. Our work is inserted in the project on forecasting ozone episodes in the Paris area realised in coorperation with AIRPARIF, the Paris area air pollution agency.

In the first part, we biefly present the ozone formation phenomena.

In the second part, we analyse the influence of wind on pollution repartition; to achieve this aim, classical data analysis (Principal Component Analysis, Procustean Analysis, Multidimensional Scaling) and linear model were used.

In the field of air pollution control, the rare event is often more significance than the common one. This is evidenced by the content of air quality standards which define acceptable upper limits of air pollution concentrations. The purpose of the third part is to establish whether observed trends in the data of tropospheric ozone are real, meaning that they could be attributed to actual changes in the emissions of toxic gases into atmosphere, or whether they are the result of meteorological changes affecting the conditions under which ozone is generated. To investigate this question, we construct a regression model in which the level of ozone is represented as a function of both meteorological variables and time, in order to determine the significance of the time component when the meteorological variables are taken into account. Also, we propose to use a logistic regression to model the probability of an exceedance of a high threshold level every day, in accounting for the relationship between very high values of ozone and meteorological conditions.Then, we apply the results of the extreme value theory to model the point process consisting of the times and the sizes of high-level exceedances by a non-homogeneous Poisson process. We apply the method to data from the Paris and Los Angeles areas.

In the fourth one, we demonstrate the convergence to a Compound Poisson process of a high-level exceedances point process ${N}_{n}\left(B\right)={\sum }_{\frac{j}{n}\in B}{1}_{{X}_{j},>{U}_{n}}$, where ${X}_{n}=\phi \left({\xi }_{n},{Y}_{n}\right),\phi$, a (regular) regression function, ${u}_{n}$ grows to infinity with $n$ in a suitable way, $\xi$ and $Y$ are mutually independent, $\xi$ is stationary and weakly dependent, and $Y$ is non-stationary, satisfying some ergodicconditions. The basic technique is the study of high-level exceedances of stationary process over suitable collections of random sets.

Keywords: Principal Component Analysis, Procustean analysis, Multidimensional Scaling, linear model, exceedances, point processes, convergence, logistic regression, diagnostic model testing, generalized Pareto distributions, meteorological conditions, non-homogeneous Poisson process, Bootstrap method, Compound Poisson process, level sets, mean occupation measures, asymptotically ponderable collections of sets.
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Bellanger, Lise. Statistique de la pollution de l'air : méthode mathématiques : applications au cas de la région parisienne. Thèses d'Orsay, no. 538 (1999), 238 p. http://numdam.org/item/BJHTUP11_1999__0538__A1_0/

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