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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]

This article explains the usage of R package tvReg, publicly available for download from the Comprehensive R Archive Network, via its application to economic and finance problems. The six basic functions in this package cover the kernel estimation of semiparametric panel data, seemingly unrelated equations, vector autoregressive, impulse response, and linear regression models whose coefficients may vary with time or any random variable. Moreover, this package provides methods for the graphical display of results, forecast, prediction, extraction of the residuals and fitted values, bandwidth selection and nonparametric estimation of the time-varying variance-covariance matrix of the error term. Applications to risk management, portfolio management, asset management and monetary policy are used as examples of these functions usage. [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]

In this work, we study the asymptotic properties of smoothed nonparametric kernel spectral density estimators for the spatial spectral density. We consider the case of continuous stationary spatial processes under a shrinking asymptotic framework. Expressions for the bias and the covariance structure are obtained and the implications for the edge effect bias of the choice of the kernel, bandwidth and spacing parameter in the design are also discussed, both for tapered and untapered estimates. Results are illustrated with a simulation study. [ABSTRACT FROM AUTHOR]