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Shrinkage estimation strategy in quasi-likelihood models

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  • Ejaz Ahmed, S.
  • Fallahpour, Saber
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    Abstract

    In this paper we consider the estimation problem for the quasi-likelihood model in presence of non-sample information (NSI). More specifically, we introduce a shrinkage estimation strategy for simultaneous model selection and parameter estimation by using the maximum quasi-likelihood estimates as the benchmark estimator, and define the pretest estimator (PTE), shrinkage estimator (SE) and positive-rule shrinkage estimator (PSE). Furthermore, we apply the lasso-type estimation strategy and compare the relative performance of lasso with the suggested estimators. The shrinkage estimators are shown to be efficient estimators compared to others. When the NSI is true the PTE has less risk compared to shrinkage and lasso estimators.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212002969
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 12 ()
    Pages: 2170-2179

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2170-2179

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    Related research

    Keywords: Shrinkage estimator; Pretest estimator; Quasi-likelihood; Asymptotic distributional bias and risk; Lasso;

    References

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    1. Kazimi, Camilla & Brownstone, David, 1999. "Bootstrap confidence bands for shrinkage estimators," Journal of Econometrics, Elsevier, vol. 90(1), pages 99-127, May.
    2. Maeyama, Yusuke & Tamaki, Kenichiro & Taniguchi, Masanobu, 2011. "Preliminary test estimation for spectra," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1580-1587, November.
    3. Ahmed, S. Ejaz & Volodin, Andrei I. & Volodin, Igor N., 2009. "High order approximation for the coverage probability by a confident set centered at the positive-part James-Stein estimator," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1823-1828, September.
    4. Gurmu, Shiferaw & Trivedi, Pravin K, 1996. "Excess Zeros in Count Models for Recreational Trips," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 469-77, October.
    5. Ahmed, S. E., 1991. "To pool or not to pool: The discrete data," Statistics & Probability Letters, Elsevier, vol. 11(3), pages 233-237, March.
    6. Christine Seller & John R. Stoll & Jean-Paul Chavas, 1985. "Validation of Empirical Measures of Welfare Change: A Comparison of Nonmarket Techniques," Land Economics, University of Wisconsin Press, vol. 62(2), pages 156-175.
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