Mathematical Sciences: Computer Intensive Methods for the Statistical Analysis of Time Series and Random Fields

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Politis The general goal of this project is to develop methods of inference for the statistical analysis of time series and random fields that do not rely on unrealistic or unverifiable model assumptions. Bootstrap resampling or computer-intensive methods offer viable approaches to obtaining valid distributional approximations while assuming very little about the stochastic mechanism generating the data. However, many important questions need to be addressed in order for these modern approaches to be applied. The main issues we wish to tackle include the following: finding general conditions for asymptotic validity of computer-intensive methods, especially subsampling, in the presence of nonstationarity; higher-order comparison of block-resampling and subsampling; developing computationally efficient and accurate estimates of standard error, and the corresponding improvement on confidence regions for parameters of interest; optimal choice of design parameters, as well as practical guidelines for implementation; assessing goodness of fit in time series settings; and finally interval estimation with random field data. The statistical analysis of time series and random fields, i.e., observations that exhibit serial (temporal) or spatial dependence, is vital in many diverse scientific disciplines, with applications in the fields of physics, engineering, acoustics, geostatistics, geophysics, medicine, econometrics, ecology, forestry, seismology, and others. The general goal of this project is to develop methods of statistical inference in the context of time series and random fields that do not rely on unrealistic or unverifiable model assumptions. The main approach that will be pursued is the utilization and refinement of the bootstrap and other computer-intensive techniques, which so far have been developed extensively and have been proven very useful in the setting of independent observations.