IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v99y2008i10p2356-2363.html
   My bibliography  Save this article

A note on cuts for contingency tables

Author

Listed:
  • Ip, Edward H.
  • Wang, Yuchung J.

Abstract

In this note, we propose a general method to find cuts for a contingency table. Useful cuts are, in many cases, statistics S-sufficient for the nuisance parameter and S-ancillary for the parameter of interest. In general, cuts facilitate a strong form of parameter separation known to be useful for conditional inference [E.L. Lehmann, Testing Statistical Hypotheses, 2nd ed., Springer, New York, 1997, pp. 546-548]. Cuts also achieve significant dimension reduction, hence, increase computational efficiency. This is particularly true for the inference about cross-tabulated data, usually with a large number of parameters. Depending on the parameter of interest, we propose a flexible transformation to reparameterize the discrete multivariate response distribution. Inference on cell probabilities or odds ratios will require different parameterizations. The reparameterized distribution is not sum-symmetric. Thus, the finding in this paper expands the results in Barndorff-Nielsen [O.E. Barndorff-Nielsen, Information and Exponential Families in Statistical Theory, John Wiley, New York, 1978, pp. 202-206].

Suggested Citation

  • Ip, Edward H. & Wang, Yuchung J., 2008. "A note on cuts for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2356-2363, November.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:10:p:2356-2363
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00065-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bent Jørgensen & Sven Jesper Knudsen, 2004. "Parameter Orthogonality and Bias Adjustment for Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 93-114, March.
    2. Christensen, B.J. & Kiefer, N.M., 1997. "Panel Data, Local Cuts, and Orthogeodesic Models," Papers 97-13, Centre for Labour Market and Social Research, Danmark-.
    3. A. C. Davison & D. A. S. Fraser & N. Reid, 2006. "Improved likelihood inference for discrete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 495-508, June.
    4. Guido Consonni & Valentina Leucari, 2006. "Reference priors for discrete graphical models," Biometrika, Biometrika Trust, vol. 93(1), pages 23-40, March.
    5. Guido Consonni & Piero Veronese, 2001. "Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 377-406, June.
    6. Nanny Wermuth & D.R. Cox, 1998. "On the Application of Conditional Independence to Ordinal Data," International Statistical Review, International Statistical Institute, vol. 66(2), pages 181-199, August.
    7. Consonni, Guido & Veronese, Piero & Gutiérrez-Peña, Eduardo, 2004. "Reference priors for exponential families with simple quadratic variance function," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 335-364, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Consonni, Guido & Massam, Hélène, 2012. "Parametrizations and reference priors for multinomial decomposable graphical models," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 380-396.
    2. Piero Veronese & Eugenio Melilli, 2015. "Fiducial and Confidence Distributions for Real Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 471-484, June.
    3. Consonni, Guido & Veronese, Piero & Gutiérrez-Peña, Eduardo, 2004. "Reference priors for exponential families with simple quadratic variance function," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 335-364, February.
    4. D. A. S. Fraser & N. Reid & E. Marras & G. Y. Yi, 2010. "Default priors for Bayesian and frequentist inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 631-654, November.
    5. Chris J. Lloyd, 2010. "Bootstrap and Second-Order Tests of Risk Difference," Biometrics, The International Biometric Society, vol. 66(3), pages 975-982, September.
    6. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2006. "Vector Multiplicative Error Models: Representation and Inference," NBER Technical Working Papers 0331, National Bureau of Economic Research, Inc.
    7. Stefano Cabras & María Castellanos & Erlis Ruli, 2014. "A Quasi likelihood approximation of posterior distributions for likelihood-intractable complex models," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 153-167, August.
    8. Martin Biehler & Heinz Holling & Philipp Doebler, 2015. "Saddlepoint Approximations of the Distribution of the Person Parameter in the Two Parameter Logistic Model," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 665-688, September.
    9. Andrew Roddam, 2001. "An approximate maximum likelihood procedure for parameter estimation in multivariate discrete data regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(2), pages 273-279.
    10. Evžen Kocenda & Martin Vojtek, 2011. "Default Predictors in Retail Credit Scoring: Evidence from Czech Banking Data," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 47(6), pages 80-98, November.
    11. Claudio Castro-López & Purificación Vicente-Galindo & Purificación Galindo-Villardón & Oscar Borrego-Hernández, 2022. "TAID-LCA: Segmentation Algorithm Based on Ternary Trees," Mathematics, MDPI, vol. 10(4), pages 1-16, February.
    12. A. C. Davison & D. A. S. Fraser & N. Reid & N. Sartori, 2014. "Accurate Directional Inference for Vector Parameters in Linear Exponential Families," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 302-314, March.
    13. Maria Victoria Ibañez & Marina Martínez-Garcia & Amelia Simó, 2021. "A Review of Spatiotemporal Models for Count Data in R Packages. A Case Study of COVID-19 Data," Mathematics, MDPI, vol. 9(13), pages 1-23, July.
    14. Lloyd, Chris J., 2010. "How close are alternative bootstrap P-values?," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1972-1976, December.
    15. Lambert, Philippe, 2021. "Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    16. Rekkas, M., 2009. "Approximate inference for the multinomial logit model," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 237-242, January.
    17. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2020. "Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 33-58, March.
    18. Webb, Emily L. & Forster, Jonathan J., 2008. "Bayesian model determination for multivariate ordinal and binary data," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2632-2649, January.
    19. Pedersen, Peder J. & Smith, Nina, 2001. "International Migration and Migration policy in Denmark," CLS Working Papers 01-5, University of Aarhus, Aarhus School of Business, Centre for Labour Market and Social Research.
    20. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2013. "Semiparametric Vector Mem," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1067-1086, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:99:y:2008:i:10:p:2356-2363. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.