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Trend in high tropospheric ozone levels. Application to Paris monitoring sites. (English) Zbl 1056.62119

Summary: This article describes the extreme value analysis of tropospheric ozone level exceedances collected at seven monitoring sites in the Paris metropolitan area during May–September over the 14-year period 1988–2001. The purpose of the study is to establish whether observed trends over time in ozone exceedances of a high threshold are real or if they are the result of meteorological changes affecting the conditions under which ozone is generated. A non-homogeneous Poisson process (NHPP), with parameters depending on meteorological covariates, temporal trend and sites factor, is used to model regionally the exceedance times and sizes of daily maxima of ozone over a high threshold. We highlight the importance of nonlinear methods to detect the nonlinearities.

MSC:

62P12 Applications of statistics to environmental and related topics
62G32 Statistics of extreme values; tail inference
62J12 Generalized linear models (logistic models)
60G35 Signal detection and filtering (aspects of stochastic processes)

Software:

ismev
Full Text: DOI

References:

[1] Bellanger L., Revue de Statistiques Appliquées pp 73– (2001)
[2] Bellanger L., Revue de Statistiques Appliquées pp 5– (2000)
[3] Bellanger L., Revue Bernoulli
[4] Chambers J. M., Statistical Models (1992)
[5] Chavez-Demoulin V., PhD thesis (1999)
[6] Coles S., An Introduction to Statistical Modeling of Extreme Values (2001) · Zbl 0980.62043 · doi:10.1007/978-1-4471-3675-0
[7] Coles S., Extremes 2 pp 5– (1999) · Zbl 0938.62013 · doi:10.1023/A:1009905222644
[8] Coles S., J. R. Statist. Soc. B 53 pp 377– (1991)
[9] Cox D. R., JRSS pp 129– (1955)
[10] Cox D. R., Point Processes (1992)
[11] Davison A. C., Statistical Extremes and Applications pp pp. 424–434– (1984)
[12] Davison A. C., J. R. Statist. Soc. 52 pp 393– (1990)
[13] Davison A. C., Bootstrap Methods and their Application (1997) · Zbl 0886.62001
[14] Davison A. C., J. R. Statist. Soc. B 62 pp pp. 191–208– (2000)
[15] Dobson A. J., An Introduction to Generalized Linear Models (2002) · Zbl 1008.62067
[16] Draper N. R. Smith H. (1981)Applied Regression Analysis2nd ed. John Wiley & Sons New York pp. 177–183
[17] Efron B., An Introduction to the Bootstrap (1993) · Zbl 0835.62038 · doi:10.1007/978-1-4899-4541-9
[18] Embrechts P., Modelling Extremal Events for Insurance and Finance (1999) · Zbl 0873.62116
[19] Falk M., Law of Small Numbers: Extremes and Rare Events (1994) · Zbl 0817.60057
[20] Hall W. J., Statistics and Related Topics pp pp. 169–184– (1981)
[21] Hastie T., Generalized Additive Models (1990) · Zbl 0747.62061
[22] Heffernan J. E., Appl. Statist. (2002)
[23] Hosking J. M. R., Technometrics 29 pp 339– (1987) · Zbl 0628.62019 · doi:10.2307/1269343
[24] Hosmer D. W., Applied Logistic Regression (2000) · Zbl 0967.62045 · doi:10.1002/0471722146
[25] Hüsler J., J. Appl. Probab. 23 pp 937– (1986) · Zbl 0614.60021 · doi:10.2307/3214467
[26] Joe H., J. R. Statist. Soc. B 54 pp 171– (1992)
[27] Kallenberg O., Random Measures (1983)
[28] Lawless J. F. (1982)Statistical Models and Methods for Lifetime DataJohn Wiley & Sons New York pp. 84–88
[29] Leadbetter M. R., Statistics Probability Lett. 12 pp 357– (1991) · Zbl 0736.60026 · doi:10.1016/0167-7152(91)90107-3
[30] Leadbetter M. R., Technical Report 9 (1993)
[31] Leadbetter M. R., Extremes and Related Properties of Random Sequences and Series (1983) · Zbl 0518.60021 · doi:10.1007/978-1-4612-5449-2
[32] McCullagh P., Generalized Linear Models (1989) · Zbl 0744.62098 · doi:10.1007/978-1-4899-3242-6
[33] Michaelis W., Air Pollution: Dimensions, Trends and Interactions with a Forest Ecosystem (1997)
[34] Nychka D., Lecture Notes in Statistics (1998)
[35] Pickands J., J. Appl. Prob. 8 pp 745– (1971) · Zbl 0242.62024 · doi:10.2307/3212238
[36] Pickands J., Ann. Statist. 3 pp 119– (1975) · Zbl 0312.62038 · doi:10.1214/aos/1176343003
[37] Reiss R. D., Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields (2001) · Zbl 1002.62002
[38] Shao J., The Jackknife and Bootstrap (1996)
[39] Shively T. S., Atmospheric Environment 24 pp 293– (1990)
[40] Shively T. S., Atmospheric Environment 25 pp 387– (1991)
[41] Smith R. L., Statistical Extremes and Applications pp pp. 621–638– (1984)
[42] Smith R. L., Biometrika 72 pp 67– (1985) · Zbl 0583.62026 · doi:10.1093/biomet/72.1.67
[43] Smith R. L., J. Hydrol. 86 pp 27– (1986) · doi:10.1016/0022-1694(86)90004-1
[44] Smith R. L., Statistical Sciences 4 pp 367– (1989) · Zbl 0955.62646 · doi:10.1214/ss/1177012400
[45] Smith R. L., National Institute for Statistical Science Technical Report #6 (1993)
[46] Smith R. L., Atmospheric Environment 29 pp 3489– (1995) · doi:10.1016/1352-2310(95)00030-3
[47] Smith R. L., Biometrika 84 pp 249– (1997) · Zbl 0891.60047 · doi:10.1093/biomet/84.2.249
[48] Snedecor G. W., Méthodes statistiques (1971)
[49] Thompson M. L., Atmospheric Environ. 35 pp 617– (2001) · doi:10.1016/S1352-2310(00)00261-2
[50] Vaquera-Huerta H., Statisitcs for the Environment 3: Pollution Assessment and Control pp pp. 175–183– (1997)
[51] Venable W. N., Statistics and Computing (1997)
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