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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Bibliographic Details
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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Summary: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.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-013-0554-6