|
Activity Number:
|
420
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Wednesday, August 9, 2006 : 10:30 AM to 12:20 PM
|
|
Sponsor:
|
Section on Physical and Engineering Sciences
|
| Abstract - #306982 |
|
Title:
|
Wavelet Variance Analysis for Random Fields
|
|
Author(s):
|
Debashis Mondal*+ and Donald B. Percival
|
|
Companies:
|
University of Washington and University of Washington
|
|
Address:
|
Department of Statistics, Box354322, Seattle, WA, 98195,
|
|
Keywords:
|
asymptotic normality ; Daubechies wavelet filter ; intrinsic random fields ; local stationarity ; maximal overlap discrete wavelet transform ; cloud data
|
|
Abstract:
|
Wavelet-based statistical methods have been used for signal and image processing, edge detection, nonparametric regression and inverse problems. Wavelets also give rise to the concept of the wavelet variance, which decomposes the sample variance of a time series and provides a time- and scale-based analysis of variance. The wavelet variance has been applied to a variety of time series and is particularly useful for studying long memory processes, detecting inhomogeneity and estimating spectral densities. Here we extend the notion of the wavelet variance to random fields and discuss large sample inference for its estimation. To illustrate our theory, we explore some specific Gaussian random fields with long range dependencies and study a localized version of the wavelet variance to test for inhomogeneity and directionality. We illustrate our methodology using images of clouds.
|
