Mathematics – Statistics Theory
Scientific paper
2007-04-09
Annals of the Institute of Statistical Mathematics (2010). Vol. 62, 299--321
Mathematics
Statistics Theory
25 pages, 5 figures
Scientific paper
10.1007/s10463-008-0171-7
We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo (MCMC) methods. When the restrictions on the combinations can be described in terms of a Segre-Veronese configuration, an explicit form of a Gr\"obner basis consisting of moves of degree two is readily available for performing a Markov chain. We illustrate our setting with the National Center Test for university entrance examinations in Japan. We also apply our method to testing independence hypotheses involving genotypes at more than one locus or haplotypes of alleles on the same chromosome.
Aoki Satoshi
Hibi Takayuki
Ohsugi Hidefumi
Takemura Akimichi
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