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Divergence-based tests of homogeneity for spatial data

The problem of testing homogeneity in contingency tables when the data are spatially correlated is considered. We derive statistics defined as divergences between unrestricted and restricted estimated joint cell probabilities and we show that they are asymptotically distributed as linear combination...

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Published in:	Statistical papers (Berlin, Germany) Germany), 2014-11, Vol.55 (4), p.1059-1077
Main Authors:	Hobza, Tomáš, Morales, Domingo, Pardo, Leandro
Format:	Article
Language:	English
Subjects:	Asymptotic properties Chi-square test Computer simulation Contingency tables Correlation Divergence Economic Theory/Quantitative Economics/Mathematical Methods Economics Finance Homogeneity Hypotheses Hypothesis testing Information theory Insurance Management Mathematical models Mathematics Mathematics and Statistics Maximum likelihood method Monte Carlo simulation Null hypothesis Operations research Operations Research/Decision Theory Probability Probability Theory and Stochastic Processes Random variables Regular Article Spatial data Statistical tests Statistics Statistics for Business Studies
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creator	Hobza, Tomáš Morales, Domingo Pardo, Leandro
description	The problem of testing homogeneity in contingency tables when the data are spatially correlated is considered. We derive statistics defined as divergences between unrestricted and restricted estimated joint cell probabilities and we show that they are asymptotically distributed as linear combinations of chi-square random variables under the null hypothesis of homogeneity. Monte Carlo simulation experiments are carried out to investigate the behavior of the new divergence test statistics and to make comparisons with the statistics that do not take into account the spatial correlation. We show that some of the introduced divergence test statistics have a significantly better behavior than the classical chi-square test for the problem under consideration when we compare them on the basis of the simulated sizes and powers.
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subjects	Asymptotic properties Chi-square test Computer simulation Contingency tables Correlation Divergence Economic Theory/Quantitative Economics/Mathematical Methods Economics Finance Homogeneity Hypotheses Hypothesis testing Information theory Insurance Management Mathematical models Mathematics Mathematics and Statistics Maximum likelihood method Monte Carlo simulation Null hypothesis Operations research Operations Research/Decision Theory Probability Probability Theory and Stochastic Processes Random variables Regular Article Spatial data Statistical tests Statistics Statistics for Business Studies
title	Divergence-based tests of homogeneity for spatial data
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