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Approximating Exact Test of Mutual Independence in Multiway Contingency Tables via Stochastic Approximation Monte Carlo
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 Title & Authors
Approximating Exact Test of Mutual Independence in Multiway Contingency Tables via Stochastic Approximation Monte Carlo
Cheon, Soo-Young;
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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.
Multi-way contingency table;exact inference;Markov chain Monte Carlo;stochastic approximation Monte Carlo;
 Cited by
Exact Inference for Three-way Interaction Effects,;

Journal of the Korean Data Analysis Society, 2013. vol.15. 1A, pp.41-51
Agresti, A. (1992). A survey of exact inference for contingency tables, Statistical Science, 7, 131-153. crossref(new window)

Agresti, A. (1999). Exact inference for categorical data: Recent advances and continuing controversies, Statistics in Medicine, 18, 2191-2207. crossref(new window)

Agresti, A. (2002). Categorical Data Analysis, 2nd edition, Wiley.

Andrieu, C., Moulines, E. and Priouret, P. (2005). Stability of stochastic approximation under verifiable conditions, SIAM Journal on Control and Optimization, 44, 283-312. crossref(new window)

Beh, E. J. and Davy, P. J. (1997). Multiple correspondence analysis of ordinal multi-way contingency tables using orthogonal polynomials, In preparation.

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. crossref(new window)

Booth, J. G. and Butler, R. W. (1999). An importance sampling algorithm for exact conditional test in log-linear models, Biometrika, 86, 321-332. crossref(new window)

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. crossref(new window)

Chen, H. F. (2002). Stochastic Approximation and Its Applications, Kluwer Academic Publishers, Dordrecht.

Deloera, J. A. and Onn, S. (2006). Markov basis of three-way tables are arbitrarily complicated, Journal of Symbolic Computation, 41, 173-181. crossref(new window)

Diaconis, P. and Sturmfels, B. (1998). Algebraic algorithms for sampling from conditional distributions, The Annals of Statistics, 26, 363-397. crossref(new window)

Dobra, A. (2003). Markov bases for decomposable graphical models, Bernoulli, 9, 1093-1108. crossref(new window)

Gastwirth, J. L. (1988). Statistical Reasoning in Law and Public Policy 1, Academic, San Diego.

Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109. crossref(new window)

Liang, F. (2009). On the use of stochastic approximation Monte Carlo for Monte Carlo integration, Statistics & Probability Letters, 79, 581-587. crossref(new window)

Liang, F., Liu, C. and Carroll, R. (2007). Stochastic approximation in Monte Carlo computation, Journal of American Statistical Association, 102, 477, 305-320. crossref(new window)

McCullagh, P. (1986). The conditional distribution of goodness-of-fit statistics for discrete data, Journal of the American Statistical Association, 81, 104-107. crossref(new window)

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. crossref(new window)

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. crossref(new window)

Robbins, H. and Monro, S. (1951). A stochastic approximation method, Annals of Mathematical Statistics, 22, 400-407. crossref(new window)

Roberts, G. O. and Tweedie, R. L. (1996). Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms, Biometrika, 83, 95-110. crossref(new window)