Computer-intensive methods for nonparametric time series analysis'

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The project focuses on the development of methods of inference for the analysis of time series and random fields that do not rely on unrealistic or unverifiable model assumptions. In particular, the investigator and his colleagues are working on: (a) extending the range of applicability of the AR-sieve bootstrap beyond the setting of linear time series; (b) devising a new Time-Frequency bootstrap procedure in which bootstrap pseudo-series are generated in the time domain although the resampling happens in the frequency domain; (c) devising a residual bootstrap scheme with larger resample size to be used for improved density estimation from time series data; (d) constructing an automatic method of efficient aggregation of spectral density estimators; (e) testing for the support of a density, as well as testing for overdifferencing and estimating the spectral density at a vanishing point; (f) devising an improved block bootstrap procedure to handle time series that are periodically or almost periodically correlated; (g) resampling and inference for locally stationary time series and inhomogeneous (but locally homogeneous) marked point processes; and (h) investigating different aspects of resampling with functional data, including the difficult problem of appropriately studentizing a functional statistic.Ever since the fundamental recognition of the potential role of the computer in modern statistics, the bootstrap and other computer-intensive statistical methods have been developed extensively for inference with independent data. Such methods are even more important in the context of dependent data where the distribution theory for estimators and tests statistics may be difficult or impractical to obtain. Furthermore, the recent information explosion has resulted in data sets of unprecedented size that call for flexible, nonparametric, computer-intensive methods of data analysis. Time series analysis in particular is vital in many diverse scientific disciplines, e.g., in economics, engineering, acoustics, geostatistics, biostatistics, medicine, ecology, forestry, seismology, and meteorology. As a consequence of the proposal's development of efficient and robust methods for the statistical analysis of dependent data, more accurate and reliable inferences may be drawn from data sets of practical import resulting into appreciable benefits to society. Examples include data from meteorology/atmospheric science, such as climate data, economics, such as stock market returns, medicine, such as EEG data, and bioinformatics, such as genomic data.