Tail estimation of the spectral density for a stationary Gaussian random field

JOURNAL OF MULTIVARIATE ANALYSIS

卷:116

Article

Wu, Wei-Ying¹  Lim, Chae Young²  Xiao, Yimin² 

[1] Natl Dong Hwa Univ, Dept Appl Math, Hualien 974, Taiwan

[2] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

关键词: Fixed-domain asymptotics;    Fractal index;    Fractal dimension;    Gaussian random fields;    Infill asymptotics;    Microergodic parameter;    Whittle likelihood;   

DOI  :  10.1016/j.jmva.2012.11.014

来源: Elsevier

【 摘 要 】

Consider a stationary Gaussian random field on R-d with spectral density f (lambda) that satisfies f(lambda) similar to c vertical bar lambda vertical bar(-0) as vertical bar lambda vertical bar -> infinity. Theparameters c and theta control the tail behavior of the spectral density. c is related to a microergodic parameter and theta is related to a fractal index. For data observed on a grid, we propose estimators of c and theta by minimizing an objective function, which can be viewed as a weighted local Whittle likelihood, study their properties under the fixed-domain asymptotics and provide simulation results. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free