Nonparametric Estimation of Spatial Risk for a Mean Nonstationary Random Field}

The common methods for spatial risk estimation are investigated for a stationary random field. Because of simplifying, lets distribution is known, and parametric variogram for the random field are considered. In this paper, we study a nonparametric spatial method for spatial risk. In this method, we model the random field trend by a local linear estimator, and through bias-corrected residuals, a valid nonparametric model was fitted to the variogram. Then the spatial risk was estimated in new locations by a bootstrap algorithm. We adopted the nonparametric spatial method to estimate conditional risk. Then, the indicator kriging was compared with a nonparametric spatial method for estimating conditional risk. Finally, these methods' behaviours have been evaluated through some simulation studies, and they were applied to analyze the meteorological data in Iran.