Computer-intensive methods for dependent observations

University dissertation from Linköping : Linköpings universitet

Abstract: This dissertation deals with computer-intensive methods for dependent observations. The main part is built up by four papers defining and analyzing a resampling method of bootstrap type for the spectral domain of a stationary Gaussian sequence. The emphasis is on practical aspects as well as on asymptotic validity. The other part develops comprehensive models for statistical extrapolation of spatially collected data. The emphasis is on practical implementation and efficient model selection.The resampling method uses known asymptotic results for the spectral parts of a sample from a stationary sequence. The resampling is done completely in the spectral domain of the sequence and has separate procedures for amplitude and phase resampling. The latter property is a new concept. Some different strategies for the two parts of the resampling are suggested, including previously suggested amplitude resampling methods. As for the phase resampling, the methods are unique for the works included in this dissertation.The performance of the method is analyzed partly by comprehensive simulation studies, partly by studying asymptotic distributions of certain estimators. The simulation results are satisfactory and the asymptotic validity is achieved. Some open questions are discussed. The development of models for extrapolation starts from different assumptions on data. The most successful modelling is by treating the data as coming from a spatial stochastic process. A parametric correlation-structure is thus applied, resulting in heavy numerical estimation routines. Another part of the modelling is the assumption of a non-linear meanvalue function of data, preferably estimated by cubic spline regression functions. To choose between the different models a comprehensive cross-validation procedure is implemented.

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