Divergence-based tests of homogeneity for spatial data
- 201 Downloads
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.
KeywordsTest of homogeneity Divergence statistics Chi-square statistic Spatial data
The authors thank the referees for careful reading of the paper and many interesting improvements. Supported by the Grants MTM2012-37077-C02-01, MTM2012-33740 and SGS12/197/OHK4/3T/14.
- Basu A, Shioya H, Park C (2011) Statistical inference: the minimum distance approach. Chapman & Hall/CRC, Boca RatonGoogle Scholar
- Cressie N (1993) Statistics for spatial data. Wiley, New YorkGoogle Scholar
- Csiszár I (1963) Eine Informationstheoretische Ungleidung und ihre Anwendung auf den Bewis del Ergodizitt on Markhoffschen Ketten. Publ Math Inst Hung Acad Sci 8:84–108Google Scholar
- Rényi A (1961) On measures of entropy and information. In: Fourth Berkeley symposium on mathematics, statistics and probability, vol. 1, pp. 547–561. University California Press, BerkeleyGoogle Scholar