Computer-Intensive Methods for Nonparametric Analysis of Dependent Data

University Of California-San Diego, La Jolla CA

Investigators

Abstract

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 into 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). The project focuses on the development of methods of inference for the analysis of dependent data that do not rely on unrealistic or unverifiable model assumptions. In particular, the principal investigator and his collaborators will work on: (a) Subsampling and resampling for Big Data, including bootstrap for multivariatetime series of large dimension; (b) New model fitting and resampling for ARMA (p,q) models with both p,q large; (c) New smoothing estimators of time-varying covariance matrices for locally stationary multivariate time series; (d) Resampling for time series with an (almost) periodic component; (e) Model-free Bootstrap for stationary and non-stationary data; (f) Estimating the degree of smoothness and support of the common density of stationary data; (g) Improved nonparametric estimation of a hazard rate function; (h) A bootstrap test for the null hypothesis of `overdifferencing'; (i) Markov-type resampling and Linear Process Bootstrap for stationary random fields; and (j) Different aspects of resampling of functional and high-dimensional time series. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.