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http://dx.doi.org/10.5351/KJAS.2012.25.5.837

Approximating Exact Test of Mutual Independence in Multiway Contingency Tables via Stochastic Approximation Monte Carlo  

Cheon, Soo-Young (Department of Informational Statistics, Korea University)
Publication Information
The Korean Journal of Applied Statistics / v.25, no.5, 2012 , pp. 837-846 More about this Journal
Abstract
Monte Carlo methods have been used in exact inference for contingency tables for a long time; however, they suffer from ergodicity and the ability to achieve a desired proportion of valid tables. In this paper, we apply the stochastic approximation Monte Carlo(SAMC; Liang et al., 2007) algorithm, as an adaptive Markov chain Monte Carlo, to the exact test of mutual independence in a multiway contingency table. The performance of SAMC has been investigated on real datasets compared to with existing Markov chain Monte Carlo methods. The numerical results are in favor of the new method in terms of the quality of estimates.
Keywords
Multi-way contingency table; exact inference; Markov chain Monte Carlo; stochastic approximation Monte Carlo;
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1 Agresti, A. (1992). A survey of exact inference for contingency tables, Statistical Science, 7, 131-153.   DOI   ScienceOn
2 Agresti, A. (1999). Exact inference for categorical data: Recent advances and continuing controversies, Statistics in Medicine, 18, 2191-2207.   DOI
3 Agresti, A. (2002). Categorical Data Analysis, 2nd edition, Wiley.
4 Andrieu, C., Moulines, E. and Priouret, P. (2005). Stability of stochastic approximation under verifiable conditions, SIAM Journal on Control and Optimization, 44, 283-312.   DOI   ScienceOn
5 Beh, E. J. and Davy, P. J. (1997). Multiple correspondence analysis of ordinal multi-way contingency tables using orthogonal polynomials, In preparation.
6 Beh, E. J. and Davy, P. J. (1998). Partitioning Pearson's chi-squared statistic for a completely ordered three-way contingency table, Australian and New Zealand Journal of Statistics, 40, 465-477.   DOI
7 Booth, J. G. and Butler, R. W. (1999). An importance sampling algorithm for exact conditional test in log-linear models, Biometrika, 86, 321-332.   DOI   ScienceOn
8 Caffo, B. S. and Booth, J. G. (2001). A Markov chain Monte Carlo algorithm for approximating exact conditional probabilities, Journal of Computational and Graphical Statistics, 10, 730-745.   DOI   ScienceOn
9 Chen, H. F. (2002). Stochastic Approximation and Its Applications, Kluwer Academic Publishers, Dordrecht.
10 Deloera, J. A. and Onn, S. (2006). Markov basis of three-way tables are arbitrarily complicated, Journal of Symbolic Computation, 41, 173-181.   DOI   ScienceOn
11 Diaconis, P. and Sturmfels, B. (1998). Algebraic algorithms for sampling from conditional distributions, The Annals of Statistics, 26, 363-397.   DOI
12 Dobra, A. (2003). Markov bases for decomposable graphical models, Bernoulli, 9, 1093-1108.   DOI   ScienceOn
13 Gastwirth, J. L. (1988). Statistical Reasoning in Law and Public Policy 1, Academic, San Diego.
14 Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109.   DOI   ScienceOn
15 Liang, F. (2009). On the use of stochastic approximation Monte Carlo for Monte Carlo integration, Statistics & Probability Letters, 79, 581-587.   DOI   ScienceOn
16 Liang, F., Liu, C. and Carroll, R. (2007). Stochastic approximation in Monte Carlo computation, Journal of American Statistical Association, 102, 477, 305-320.   DOI   ScienceOn
17 McCullagh, P. (1986). The conditional distribution of goodness-of-fit statistics for discrete data, Journal of the American Statistical Association, 81, 104-107.   DOI   ScienceOn
18 Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equations of state calculations by fast computing machines, Journal of Chemical Physics, 21, 1087-1091.   DOI
19 Paul, S. and Deng, D. (2000). Goodness of fit of generalized linear models to sparse data, Journal of the Royal Statistical Society, Series B, 62, 323-333.   DOI   ScienceOn
20 Robbins, H. and Monro, S. (1951). A stochastic approximation method, Annals of Mathematical Statistics, 22, 400-407.   DOI
21 Roberts, G. O. and Tweedie, R. L. (1996). Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms, Biometrika, 83, 95-110.   DOI   ScienceOn