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) consistent estimation of the matrix-valued autocovariance sequence of a multivariate stationary time series, and a subsequent linear process bootstrap procedure that is valid even in the context of high-dimensional processes; (b) flat-top kernels and their application to improved nonparametric estimation of a hazard rate function and to aggregation of spectral density estimators; (c) testing for the support of a probability density and testing for over-differencing of a time series; (d) a new block bootstrap procedure for time series that are periodically or almost periodically correlated; (e) estimation and testing in the context of locally stationary time series and resampling inference for possibly inhomogeneous marked point processes; and (f) different aspects of resampling with functional data, including the difficult open 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 test statistics may be difficult or impractical to obtain. Furthermore, the recent information explosion has resulted in datasets of unprecedented size that call for flexible, nonparametric, and--by necessity--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 datasets of practical import resulting in appreciable benefits to society. Examples include data from meteorology/atmospheric science (e.g. climate data), economics (e.g. stock market returns), biostatistics (e.g. fMRI data), and bioinformatics (e.g. genetics and microarray data).
