| Summary: | 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.
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