Resampling Methods for Temporal and Spatial Processes

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ABSTRACTThe project consists of two parts, viz., (1) Developing a class bootstrap methods, called the "Transform Based Bootstrap", for long-range dependent data and studying their properties; and (2) Developing a class resampling methods, called the "Varying Probability Spatial Block Bootstrap" and "Varying Probability Spatial Subsampling" for spatial data under some (nonstandard) spatial sampling designs. Although a number of resampling methods have been proposed and shown to be effective in dealing with weak dependence in time series data, an earlier work of the PI reveals that these methods have only limited success under long range dependence. Since long-range dependent data appear naturally and frequently in many scientific studies (cf. Kuensch, H.R., Beran, J., and Hampel, F. (1993; Annals of Statistics)), developing effective resampling methods for such data is important. The transform-based-bootstrap, proposed here, holds some promise. The other part of the project deals with spatial data. Unlike the time-series case where the random process evolves only in one direction, processes with a continuous spatial index allow for more than one evolution pattern. This leads to different types of (often nonstandard) asymptotics for spatial data. The proposed project seeks to develop new resampling methods for spatial data in such cases, particularly for irregularly spaced data-sites.The emphasis of the proposed project is on development of suitable resampling methods for time-series and spatial data having a complex structure and on investigating their properties. Current statistical methodology for dependent data are predominantly parametric model based and are sensitive to model misspecification. The proposed research seeks to address this need and is aimed at removing some of the limitations of the current methodology.