Resampling Methodology in Spatial Prediction and Repeated Measures Time Series

Abstract

In recent years, the application of resampling methods to dependent data, such as time series or spatial data, has been a growing field in the study of statistics. In this dissertation, we discuss two such applications. In spatial statistics, the reliability of Kriging prediction methods relies on the observations coming from an underlying Gaussian process. When the observed data set is not from a multivariate Gaussian distribution, but rather is a transformation of Gaussian data, Kriging methods can produce biased predictions. Bootstrap resampling methods present a potential bias correction. We propose a parametric bootstrap methodology for the calculation of either a multiplicative or additive bias correction factor when dealing with Trans-Gaussian data. Furthermore, we investigate the asymptotic properties of the new bootstrap based predictors. Finally, we present the results for both simulated and real world data. In time series analysis, the estimation of covariance parameters is often of utmost importance. Furthermore, the understanding of the distributional behavior of parameter estimates, particularly the variance, is useful but often difficult. Block bootstrap methods have been particularly useful in such analyses. We introduce a new procedure for the estimation of covariance parameters for replicated time series data.