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A Family of Quasisymmetry Models

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Abstract (2. Language): 
We present a one-parameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its Pearsonian analogue. Algebraically, this corresponds to deformations of toric ideals associated with graphs. Our discussion of the statistical issues centers around maximum likelihood estimation.
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REFERENCES

References: 

[1] Shun-ichi Amari and Andrzej Cichocki. Information geometry of divergence functions.
Bulletin of the Polish Academy of Sciences: Technical Sciences, 58(1):183{195, 2010.
[2] Yvonne M. Bishop, Stephen E. Fienberg, and Paul W. Holland. Discrete multivariate
analysis: theory and practice. Springer Science & Business Media, 2007.
[3] Albert H. Bowker. A test for symmetry in contingency tables. Journal of the american
statistical association, 43(244):572{574, 1948.
[4] Henri Caussinus. Contribution a l'analyse statistique des tableaux de correlation. In
Annales de la Faculte des Sciences de Toulouse, volume 29, pages 77{183. Universite Paul
Sabatier, 1965.
[5] Mathias Drton, Bernd Sturmfels, and Seth Sullivant. Lectures on algebraic statistics.
Springer Science & Business Media, 2008.
[6] Maria Kateri and Alan Agresti. A generalized regression model for a binary response.
Statistics & Probability Letters, 80(2):89{95, 2010.
[7] Maria Kateri and Takis Papaioannou. Asymmetry models for contingency tables. Journal
of the American Statistical Association, 92(439):1124{1131, 1997.
[8] Ezra Miller and Bernd Sturmfels. Combinatorial commutative algebra, volume 227 of Graduate
Texts in Mathematics. Springer-Verlag, New York, 2005.
[9] Lior Pachter and Bernd Sturmfels. Algebraic statistics for computational biology, volume 13.
Cambridge University Press, 2005.
[10] Leandro Pardo. Statistical inference based on divergence measures. CRC Press, 2005.
[11] Fabio Rapallo. Algebraic markov bases and mcmc for two-way contingency tables. Scandinavian
journal of statistics, 30(2):385{397, 2003.
[12] Alan Stuart. The estimation and comparison of strengths of association in contingency
tables. Biometrika, pages 105{110, 1953.
[13] Bernd Sturmfels. Grobner bases and convex polytopes, University Lecture Series, vol. 8,
Providence, RI. 1996.

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