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Pretest and shrinkage estimation of the regression parameter vector of the marginal model with multinomial responses

Author

Listed:
  • Marwan Al-Momani

    (University of Sharjah)

  • M. Riaz

    (King Fahd University of Petroleum & Minerals)

  • M. F. Saleh

    (King Fahd University of Petroleum & Minerals)

Abstract

Generalized Estimating Equations (GEE) approach has become a popular method that is applied for correlated categorical multinomial responses data in clinical trials and other biomedical experiments. GEEs estimates of the marginal regression parameter vector are consistent. In this article, we propose the pretest, shrinkage, and positive shrinkage estimators for the regression vector of the marginal model with multinomial responses. The array of estimators are compared analytically via their asymptotic quadratic risks, and numerically via their simulated relative efficiencies. We apply the proposed estimation technique to two real data examples and employed a bootstrapping approach to computing the bootstrapping mean squared error of the estimators.

Suggested Citation

  • Marwan Al-Momani & M. Riaz & M. F. Saleh, 2023. "Pretest and shrinkage estimation of the regression parameter vector of the marginal model with multinomial responses," Statistical Papers, Springer, vol. 64(6), pages 2101-2117, December.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01372-2
    DOI: 10.1007/s00362-022-01372-2
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    References listed on IDEAS

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    1. Marwan Al-Momani & Abdulkadir A. Hussein & S. E. Ahmed, 2017. "Penalty and related estimation strategies in the spatial error model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(1), pages 4-30, January.
    2. Xiaoli Gao & S. Ejaz Ahmed & Yang Feng, 2017. "Rejoinder to ‘Post‐selection shrinkage estimation for high‐dimensional data analysis’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(2), pages 131-135, March.
    3. Touloumis, Anestis, 2015. "R Package multgee: A Generalized Estimating Equations Solver for Multinomial Responses," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i08).
    4. Xiaoli Gao & S. E. Ahmed & Yang Feng, 2017. "Post selection shrinkage estimation for high‐dimensional data analysis," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(2), pages 97-120, March.
    5. Anestis Touloumis & Alan Agresti & Maria Kateri, 2013. "GEE for Multinomial Responses Using a Local Odds Ratios Parameterization," Biometrics, The International Biometric Society, vol. 69(3), pages 633-640, September.
    6. Peihua Qiu & Kai Yang & Lu You, 2017. "Discussion of ‘Post selection shrinkage estimation for high‐dimensional data analysis’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(2), pages 123-125, March.
    7. Marwan Al-Momani & Abdaljbbar B. A. Dawod, 2022. "Model Selection and Post Selection to Improve the Estimation of the ARCH Model," JRFM, MDPI, vol. 15(4), pages 1-17, April.
    8. Sévérien Nkurunziza & Marwan Al-Momani & Eric Yu Yin Lin, 2016. "Shrinkage and LASSO strategies in high-dimensional heteroscedastic models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(15), pages 4454-4470, August.
    9. Yanming Li & Hyokyoung Grace Hong & Yi Li, 2017. "Discussion of ‘Post selection shrinkage estimation for high‐dimensional data analysis’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(2), pages 126-129, March.
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