An Example of Inconsistent MLE of Spatial Covariance Parameters under Increasing Domain Asymptotics
نویسنده
چکیده
Asymptotic properties of estimators of covariance parameters in spatial statistics are commonly considered under the frameworks of increasing domain and fixed domain asymptotics, respectively. Although inconsistency is a general conclusion under the framework of fixed domain asymptotics, it is generally believed that consistency should generally hold under the framework of increasing domain asymptotics. This article provides an example in which the maximum likelihood estimator (MLE) of covariance parameters is still inconsistent under the framework of increasing domain asymptotics. Therefore, consistency may still be a problem under the framework of increasing domain asymptotics.
منابع مشابه
Infill Asymptotics for a Stochastic Process Model with Measurement Error
In spatial modeling the presence of measurement error, or “nugget”, can have a big impact on the sample behavior of the parameter estimates. This article investigates the nugget effect on maximum likelihood estimators for a onedimensional spatial model: Ornstein-Uhlenbeck plus additive white noise. Consistency and asymptotic distributions are obtained under infill asymptotics, in which a compac...
متن کاملFixed-domain Asymptotic Properties of Tapered Maximum Likelihood Estimators
When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. Under the assumption that data are collected along a line in a bounded region, we investigate how the tapering affects the asymptotic efficiency o...
متن کاملHeteroskedasticity of Unknown Form in Spatial Autoregressive Models with a Moving Average Disturbance Term
In this study, I investigate the necessary condition for the consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. I also show that the MLE of pa...
متن کاملTapered Covariance: Bayesian Estimation and Asymptotics
The method of maximum tapered likelihood has been proposed as a way to quickly estimate covariance parameters for stationary Gaussian random fields. We show that under a useful asymptotic regime, maximum tapered likelihood estimators are consistent and asymptotically normal for covariance models in common use. We then formalize the notion of tapered quasi-Bayesian estimators and show that they ...
متن کاملA Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data
The Gaussian geostatistical model has been widely used in modeling of spatial data. However, it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix, particularly when there is a large number of observations. This article proposes a resampling-based stochastic approximation method to address this challenge. At each iteration of t...
متن کامل