Bootstrap Methods To Evaluate The Efficiency Of The Estimators Of The Spatial Unilateral Ar(1,1) Model
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Date
2011-12
Authors
Siregar, Latifah Rahayu
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Three categories of the spatial data are geostatistical data, lattice data and
point pattern data. This thesis focuses on the estimation aspect of the spatial
unilateral autoregressive models for spatial lattice data on two-dimensional regular
grid. Specifically, this thesis evaluate the efficiency of the estimators of the first
order spatial unilateral autoregressive model, AR(1,1) using the bootstrapping
methods. A comparative studies are done to compare the performance among the
available methods for estimating the parameters of AR(1,1) model, namely the Yule-
Walker, the unbiased Yule-Walker, the least squares and the maximum likelihood
methods. Two types of bootstrap methods are considered, namely bootstrapping the
residual and block bootstrap, which are commonly used in time series analysis. The
standard error of the estimate is used as criterion to assess the efficiency of the
estimators. To indicate the reliability of the estimate, the standard confidence
intervals are constructed. The differences of the performance between two types of
bootstrap methods are also being examined. In addition, the numerical examples are
also given to illustrate the procedure of the bootstrapping methods to assess the
efficiency of the estimators. The results of the thesis show that, in general, the Yule-
Walker estimate is more efficient as compared to the other estimates and
bootstrapping the residual method is easier and more consistent than the block
bootstrap method.
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Keywords
Bootstrap methods to evaluate , the efficiency of the estimators