Computer-Intensive Methods for Nonparametric Analysis of Dependent Data

University Of California-San Diego, La Jolla CA

Investigators

Abstract

Ever since the recognition of the 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, computer-intensive methods of data analysis. Time series analysis in particular is vital in many diverse scientific disciplines, including economics, engineering, acoustics, geostatistics, biostatistics, medicine, ecology, forestry, seismology, and meteorology. This research project aims to develop efficient and robust methods for the statistical analysis of dependent data that will enable more accurate and reliable inferences to 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). 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 colleagues are working on: (a) Markov-type resampling and linear process bootstrap for stationary random fields; (b) local block bootstrap for inference with inhomogeneous marked point processes; (c) estimation of the degree of smoothness and support of the common density of stationary data; (d) improved nonparametric estimation via the use of flat-top kernels; (e) a bootstrap test for the null hypothesis of time series "over-differencing;" (f) seasonal block bootstrap for almost-periodic data; (g) model-free point predictors and prediction intervals for locally stationary time series; (h) smooth estimation of time-varying covariance matrices for locally stationary multivariate time series; and (i) different aspects of resampling with functional data, including the difficult open problem of appropriately studentizing a functional statistic.