Mathematical Sciences: Resampling Methods Under Long Range Dependence

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Proposal: DMS 9505124 PI: Saumendra Lahiri Institution: Iowa State University Title: Resampling Methods Under Long Range Dependence ABSTRACT: The main thrust of the research is to develop suitable resampling schemes and to study their properties for data exhibiting very strong forms of dependence. It is well known that existing resampling schemes perform very poorly under such dependence structures. Two new resampling schemes for long-range dependent data are investigated. These schemes are a sampling-window method based on subsamples of the data and a bootstrap method based on finite Fourier transformations. Their effectiveness in different inference problems is examined. The phenomenon of long range dependence, such as the concentration of an air-pollutant in a city observed at closely located sites, occurs when the data are highly correlated. This sort of data has a high level of variability, even after averaging. The research involves developing suitable resampling schemes for long-range dependent data that will provide good statistical estimates. The research has direct applications in Hydrology, Geology, Economics, and Environmental problems.