You are here

Connectivity for 3 x 3 x K contingency tables

Journal Name:

Publication Year:

AMS Codes:

Abstract (2. Language): 
We consider an exact sequential conditional test for three-way conditional test of no interaction. At each time  , the test uses as the conditional inference frame the set F(H ) of all tables with the same three two-way marginal tables as the obtained table H . For 33K tables, we propose a method to construct F(H ) from F(H
54-74

REFERENCES

References: 

[1] A Agresti. An introduction to categorical data analysis. Wiley Series in Probability
and Statistics, 2nd edition, Wiley-Interscience, 2007.
REFERENCES 74
[2] S Aoki. Exact methods and Markov chain Monte Carlo methods of conditional infer-
ence for contingency tables. PhD thesis, Tokyo University, 2004.
[3] S Aoki and A Takemura. Minimal basis for connected Markov chain over 3 3 k
contingency tables with xed two-dimensional marginals. Australian and New Zealand
Journal of Statistics, 45:229{249, 2003.
[4] S Aoki, A Takemura and R Yoshida. Indispensable monomials of toric ideals and
Markov bases. Journal of Symbolic Computation, 43:490{507, 2008.
[5] F Bunea and J. E. Besag. MCMC in I J K contingency tables. In Monte Carlo
Methods (ed. N. Madras), Fields Institute Communications, 26:25{36, 2000.
[6] P Diaconis and B Sturmfels. Algebraic algorithms for sampling from conditional
distributions. Ann. Statist., 26:363{397, 1998.
[7] J De Loera and S Onn. Markov bases of three-way tables are arbitrarily complicated.
Journal of Symbolic Computation, 41:173{181, 2006.
[8] C P Robert and G Casella. Monte Carlo statistical methods. Springer Texts in
Statistics., Springer-Verlag, New York, 2004.
[9] B Sturmfels, M Drton and S Sullivant. Lecture on algebraic statistics. Birkhauser,
2009.
[10] T Sakata and R Sawae. A study of the sequential conditional test for contingency
tables. Journal of the Japanese Society of Computational Statistics, 15:169{174, 2003.
[11] T Sakata and T Sumi. Lifting between the sets of three-way contingency tables and r-
neighbourhood property. In Electric Proceedings of COMPSTAT '2008., pages 87{94,
2008.
[12] B Sturmfels. Grobner bases and convex polytopes. American Mathematical Society,
University Lecture Series 8, 1996.
[13] T Sumi and T Sakata. 2-neighborhood theorem for 3 3 3 contingency tables.
Journal of the Indian Society for Probability and Statistics, in press, 2011.

Thank you for copying data from http://www.arastirmax.com