Computer-intensive Methods for the Statistical Analysis of Dependent Data

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Politis 9703964 This project involves the on-going development of resampling and subsampling as they apply to dependent data, i.e., time series, random fields, and (marked) point processes. The investigator's efforts redirected towards: (a) relaxing the conditions for asymptotic validity of computer-intensive methods for dependent data (e.g., allow for nonstationarity, slow mixing rate, etc.); (b) rendering subsampling more `automatic' by devising a built-in procedure for estimation of the rate of convergence of the statistic in question; (c) improving the accuracy of distribution estimation by techniques such as Richardson extrapolation, and by optimal choice of block size; (d) developing appropriate resampling/subsampling methods in the case of alternative data-collection scenarios as is the case of measurements at irregularly spaced locations, i.e., data from a marked point process; and (e) exploring the idea of `local' resampling for time series. This research focuses on the development of computer-intensive methods of statistical inference for the analysis of dependent data without having to rely on unrealistic or unverifiable model assumptions. The statistical analysis of dependent data is vital in many diverse scientific disciplines; thus this research has potentially many practical applications. For example, consider the problem of stochastic computer simulation of complex manufacturing systems that is an important issue in Industrial Engineering; the methodology of subsampling for `almost' stationary time series is most helpful in order to assess convergence and accuracy of the simulation. For another example, suppose that X(t) denotes an environmental measurement, e.g., rain precipitation or ozone concentration as measured at location t. Typically, the t-points where X(t) is measured are irregularly scattered in space or on the earth's surface. The development of a general methodology for statistical inference involving data of this type is a significant contribution i n spatial statistics and, in particular, studies involving geological, atmospheric, and environmental data.