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Year 2020, Volume: 49 Issue: 4, 1480 - 1492, 06.08.2020
https://doi.org/10.15672/hujms.560405

Abstract

References

  • [1] A. Agresti, Categorical Data Analysis, J. Wiley, Hoboken, New Jersey, 2002.
  • [2] F. Bartolucci and A. Forcina, Extended RC association models allowing for order restrictions and marginal modeling, J. Amer. Statist. Associ., 97, 1192-1199, 2002.
  • [3] M.P. Becker and A. Agresti, Maximum likelihood estimation of the RC(M) association model, Appl. Statist., 39, 152-167, 1992.
  • [4] M.P. Becker and C. Clogg, Analysis of sets of two-way contingency tables using association models, J. Amer. Statist. Asso., 84, 142-151, 1989.
  • [5] Y.M. Bishop, S.E. Fienberg, and P.W. Holland, Discrete Multivariate Analysis: Theory and Applications, Springer, 2007.
  • [6] V.V. Buldygin and V.Y. Kozachnko, Subgaussian random variables, Ukrainian Math. J., 32, 483-489, 1980.
  • [7] T.T. Cai and A. Zhang, Inferencial for high-dimensional differential correlation matrices, J. of Multivariate Analysis, 143, 107-126, 2016.
  • [8] T.T. Cai and H.H. Zhou, Optimal rates of convergence for sparse covariance matrix estimation, Ann. Statist., 40(5), 2389-2420 2012.
  • [9] S.K. Ghoreishi and M.R. Meshkani, Bayesian analysis of association (BANOAS) in contingency tables with ordinal and interval variables, J. of Statistical Theory and Applications, 5(2), 363-372, 2006.
  • [10] S.K. Ghoreishi and M.R. Meshkani, Asymptotic Maximum Likelihood and Bayesian Analysis of Shares of Various Weighted Trends in Association Models in Contingency Tables, J. of Statistical Theory and Applications, 7(2), 229-243, 2008.
  • [11] L.O. Goodman, Simple models for the analysis of association in cross-classifications having ordered categories, J. Amer. Statist. Associ., 74, 537-552, 1979.
  • [12] L.O. Goodman, The analysis of cross-classified data having ordered and/or unordered categories: association models, correlation models and asymmetry models for contingency tables with or without missing entries, Ann. statist., 13, 10-69, 1985.
  • [13] L.O. Goodman, Measures, models, and graphical displays in the analysis of crossclassified data, J. Amer. Statist. Assoc., 86, 1085-1111, 1991.
  • [14] M. Kateri, T. Papaioannou, and R. Ahmad, New association models for the analysis of sets of two-way contingency tables, Statistica Applica, 8, 537-551, 1996.
  • [15] M. Kateri, R. Ahmad, and T. Papaioannou, New features in the class of association models, Applied Stochastic models and Data Analysis, 14, 125-136, 1998.
  • [16] A. Rothman, E. Levina, and J. Zhu, Generalized thresholding of large covariance matrices, J. Amer. Statist. Associ., 104, 177-186, 2009.

Adaptive thresholding estimator for differential association structures in two independent contingency tables

Year 2020, Volume: 49 Issue: 4, 1480 - 1492, 06.08.2020
https://doi.org/10.15672/hujms.560405

Abstract

In this paper, we consider an adaptive thresholding procedure to estimate the difference of association structures in two independent two-way contingency tables of the same order. Here, we assume that the class of paired association structures have an approximately sparse difference. Under $L_1$ and $L_2$ loss functions, we establish the corresponding risk's upper bounds for our differential association adaptive thresholding estimators. Moreover, we show that these estimators perform well in a simulated setting. In this line, we carry out a simulation study and compare two well-known independent social mobility datasets.

References

  • [1] A. Agresti, Categorical Data Analysis, J. Wiley, Hoboken, New Jersey, 2002.
  • [2] F. Bartolucci and A. Forcina, Extended RC association models allowing for order restrictions and marginal modeling, J. Amer. Statist. Associ., 97, 1192-1199, 2002.
  • [3] M.P. Becker and A. Agresti, Maximum likelihood estimation of the RC(M) association model, Appl. Statist., 39, 152-167, 1992.
  • [4] M.P. Becker and C. Clogg, Analysis of sets of two-way contingency tables using association models, J. Amer. Statist. Asso., 84, 142-151, 1989.
  • [5] Y.M. Bishop, S.E. Fienberg, and P.W. Holland, Discrete Multivariate Analysis: Theory and Applications, Springer, 2007.
  • [6] V.V. Buldygin and V.Y. Kozachnko, Subgaussian random variables, Ukrainian Math. J., 32, 483-489, 1980.
  • [7] T.T. Cai and A. Zhang, Inferencial for high-dimensional differential correlation matrices, J. of Multivariate Analysis, 143, 107-126, 2016.
  • [8] T.T. Cai and H.H. Zhou, Optimal rates of convergence for sparse covariance matrix estimation, Ann. Statist., 40(5), 2389-2420 2012.
  • [9] S.K. Ghoreishi and M.R. Meshkani, Bayesian analysis of association (BANOAS) in contingency tables with ordinal and interval variables, J. of Statistical Theory and Applications, 5(2), 363-372, 2006.
  • [10] S.K. Ghoreishi and M.R. Meshkani, Asymptotic Maximum Likelihood and Bayesian Analysis of Shares of Various Weighted Trends in Association Models in Contingency Tables, J. of Statistical Theory and Applications, 7(2), 229-243, 2008.
  • [11] L.O. Goodman, Simple models for the analysis of association in cross-classifications having ordered categories, J. Amer. Statist. Associ., 74, 537-552, 1979.
  • [12] L.O. Goodman, The analysis of cross-classified data having ordered and/or unordered categories: association models, correlation models and asymmetry models for contingency tables with or without missing entries, Ann. statist., 13, 10-69, 1985.
  • [13] L.O. Goodman, Measures, models, and graphical displays in the analysis of crossclassified data, J. Amer. Statist. Assoc., 86, 1085-1111, 1991.
  • [14] M. Kateri, T. Papaioannou, and R. Ahmad, New association models for the analysis of sets of two-way contingency tables, Statistica Applica, 8, 537-551, 1996.
  • [15] M. Kateri, R. Ahmad, and T. Papaioannou, New features in the class of association models, Applied Stochastic models and Data Analysis, 14, 125-136, 1998.
  • [16] A. Rothman, E. Levina, and J. Zhu, Generalized thresholding of large covariance matrices, J. Amer. Statist. Associ., 104, 177-186, 2009.
There are 16 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Seyed Kamran Ghoreishi 0000-0003-4998-6707

Jingjing Wu This is me 0000-0003-4555-1490

Publication Date August 6, 2020
Published in Issue Year 2020 Volume: 49 Issue: 4

Cite

APA Ghoreishi, S. K., & Wu, J. (2020). Adaptive thresholding estimator for differential association structures in two independent contingency tables. Hacettepe Journal of Mathematics and Statistics, 49(4), 1480-1492. https://doi.org/10.15672/hujms.560405
AMA Ghoreishi SK, Wu J. Adaptive thresholding estimator for differential association structures in two independent contingency tables. Hacettepe Journal of Mathematics and Statistics. August 2020;49(4):1480-1492. doi:10.15672/hujms.560405
Chicago Ghoreishi, Seyed Kamran, and Jingjing Wu. “Adaptive Thresholding Estimator for Differential Association Structures in Two Independent Contingency Tables”. Hacettepe Journal of Mathematics and Statistics 49, no. 4 (August 2020): 1480-92. https://doi.org/10.15672/hujms.560405.
EndNote Ghoreishi SK, Wu J (August 1, 2020) Adaptive thresholding estimator for differential association structures in two independent contingency tables. Hacettepe Journal of Mathematics and Statistics 49 4 1480–1492.
IEEE S. K. Ghoreishi and J. Wu, “Adaptive thresholding estimator for differential association structures in two independent contingency tables”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, pp. 1480–1492, 2020, doi: 10.15672/hujms.560405.
ISNAD Ghoreishi, Seyed Kamran - Wu, Jingjing. “Adaptive Thresholding Estimator for Differential Association Structures in Two Independent Contingency Tables”. Hacettepe Journal of Mathematics and Statistics 49/4 (August 2020), 1480-1492. https://doi.org/10.15672/hujms.560405.
JAMA Ghoreishi SK, Wu J. Adaptive thresholding estimator for differential association structures in two independent contingency tables. Hacettepe Journal of Mathematics and Statistics. 2020;49:1480–1492.
MLA Ghoreishi, Seyed Kamran and Jingjing Wu. “Adaptive Thresholding Estimator for Differential Association Structures in Two Independent Contingency Tables”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, 2020, pp. 1480-92, doi:10.15672/hujms.560405.
Vancouver Ghoreishi SK, Wu J. Adaptive thresholding estimator for differential association structures in two independent contingency tables. Hacettepe Journal of Mathematics and Statistics. 2020;49(4):1480-92.