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The objective is to provide a nonparametric bootstrap method for functional data that consists of independent realizations of a continuous one-dimensional process. The process is assumed to be nonstationary, with a functional mean and a functional variance, and dependent. The resampling method is based on nonparametric estimates of the model components. Numerical studies were conducted to check the performance of the proposed procedure, by approximating the bias and the standard error of two estimators. A practical application of the proposed approach to pollution data has also been included. Specifically, it is employed to make inference about the annual trend of ground-level ozone concentration at Yarner Wood monitoring station in the United Kingdom. Supplementary material to this paper is provided online. [ABSTRACT FROM AUTHOR]

A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation techniques with nonparametric estimations of the trend and the variability. The nonparametric local linear estimator, considering a bandwidth matrix selected by a method that takes the spatial dependence into account, is used to estimate the trend. The variability is modeled estimating the conditional variance and the variogram from corrected residuals to avoid the biasses. The proposed method allows to obtain estimates of the conditional exceedance risk in non-observed spatial locations. The performance of the approach is analyzed by simulation and illustrated with the application to a real data set of precipitations in the USA.Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

In this work, a fully nonparametric geostatistical approach to estimate threshold exceeding probabilities is proposed. To estimate the large-scale variability (spatial trend) of the process, the nonparametric local linear regression estimator, with the bandwidth selected by a method that takes the spatial dependence into account, is used. A bias-corrected nonparametric estimator of the variogram, obtained from the nonparametric residuals, is proposed to estimate the small-scale variability. Finally, a bootstrap algorithm is designed to estimate the unconditional probabilities of exceeding a threshold value at any location. The behavior of this approach is evaluated through simulation and with an application to a real data set. [ABSTRACT FROM AUTHOR]