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In this paper, nonparametric curve estimation methods are applied to analyze time series of wind speeds, focusing on the extreme events exceeding a chosen threshold. Classical parametric statistical approaches in this context consist in fitting a generalized Pareto distribution (GPD) to the tail of the empirical cumulative distribution, using maximum likelihood or the method of the moments to estimate the parameters of this distribution. Additionally, confidence intervals are usually computed to assess the uncertainty of the estimates. Nonparametric methods to estimate directly some quantities of interest, such as the probability of exceedance, the quantiles or return levels, or the return periods, are proposed. Moreover, bootstrap techniques are used to develop pointwise and simultaneous confidence intervals for these functions. The proposed models are applied to wind speed data in the Gulf Coast of US, comparing the results with those using the GPD approach, by means of a split-sample test. Results show that nonparametric methods are competitive with respect to the standard GPD approximations. The study is completed generating synthetic data sets and comparing the behavior of the parametric and the nonparametric estimates in this framework. [ABSTRACT FROM AUTHOR]

Abstract: Controlling emissions of air pollutants and establishing air quality objectives to improve and protect ambient air quality are very important tasks of Governments. Ozone (O3), one of those pollutants of concern, is not emitted directly into the atmosphere, but is a secondary pollutant produced by reaction between nitrogen dioxide (NO2), hydrocarbons and sunlight. High levels of ozone can produce harmful effects on human health and the environment in general. Therefore, the study of extreme values of ozone represents an important topic of research in environmental problems. Classical extreme value theory has been usually used in air-pollution studies. It consists of fitting a parametric generalized extreme value (GEV) distribution to a data set of extreme values and using the estimated distribution to compute quantities like the probability of exceedance, the quantiles, the return levels or the mean return periods. In this paper, we propose nonparametric methods to estimate those quantities. Additionally, nonparametric estimators of the trends of very high values of ozone are proposed. The nonparametric estimators are applied to real samples of maximum ozone values obtained from several monitoring stations belonging to the Automatic Urban and Rural Network (AURN) from the UK. Results show that nonparametric estimators work satisfactorily, generally outperforming the behaviour of classical parametric estimators. [ABSTRACT FROM AUTHOR]

Abstract: The study of extreme values and prediction of ozone data is an important topic of research when dealing with environmental problems. Classical extreme value theory is usually used in air-pollution studies. It consists in fitting a parametric generalised extreme value (GEV) distribution to a data set of extreme values, and using the estimated distribution to compute return levels and other quantities of interest. Here, we propose to estimate these values using nonparametric functional data methods. Functional data analysis is a relatively new statistical methodology that generally deals with data consisting of curves or multi-dimensional variables. In this paper, we use this technique, jointly with nonparametric curve estimation, to provide alternatives to the usual parametric statistical tools. The nonparametric estimators are applied to real samples of maximum ozone values obtained from several monitoring stations belonging to the Automatic Urban and Rural Network (AURN) in the UK. The results show that nonparametric estimators work satisfactorily, outperforming the behaviour of classical parametric estimators. Functional data analysis is also used to predict stratospheric ozone concentrations. We show an application, using the data set of mean monthly ozone concentrations in Arosa, Switzerland, and the results are compared with those obtained by classical time series (ARIMA) analysis. [ABSTRACT FROM AUTHOR]