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A note on improving quadratic inference functions using a linear shrinkage approach


  • Han, Peisong
  • Song, Peter X.-K.


In some commonly used longitudinal clinical trials designs, the quadratic inference functions (QIF) method fails to work due to non-invertible estimation of the optimal weighting matrix. We propose a modified QIF method, in which the optimal weighting matrix is estimated by a linear shrinkage estimator, replacing the sample covariance matrix. We prove that the linear shrinkage estimator is consistent and asymptotically optimal under the expected quadratic loss, and will have more stable numerical performance than the sample covariance matrix. Simulations show that numerical improvements are acquired in light of a higher percentage of convergence, and smaller standard errors and mean square errors of parameter estimates.

Suggested Citation

  • Han, Peisong & Song, Peter X.-K., 2011. "A note on improving quadratic inference functions using a linear shrinkage approach," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 438-445, March.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:3:p:438-445

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    References listed on IDEAS

    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Annie Qu, 2004. "Assessing robustness of generalised estimating equations and quadratic inference functions," Biometrika, Biometrika Trust, vol. 91(2), pages 447-459, June.
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    Cited by:

    1. Westgate, Philip M., 2013. "A bias-corrected covariance estimator for improved inference when using an unstructured correlation with quadratic inference functions," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1553-1558.


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