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A Simple Formula for Mixing Estimators With Different Convergence Rates

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  • Stephen S. M. Lee
  • Mehdi Soleymani

Abstract

Suppose that two estimators, and , are available for estimating an unknown parameter θ, and are known to have convergence rates n -super-1/2 and r n = o ( n -super-1/2), respectively, based on a sample of size n . Typically, the more efficient estimator is less robust than , and a definitive choice cannot be easily made between them under practical circumstances. We propose a simple mixture estimator, in the form of a linear combination of and , which successfully reaps the benefits of both estimators. We prove that the mixture estimator possesses a kind of oracle property so that it captures the fast n -super-1/2 convergence rate of when conditions are favorable, and is at least r n -consistent otherwise. Applications of the mixture estimator are illustrated with examples drawn from different problem settings including orthogonal function regression, local polynomial regression, density derivative estimation, and bootstrap inferences for possibly dependent data.

Suggested Citation

  • Stephen S. M. Lee & Mehdi Soleymani, 2015. "A Simple Formula for Mixing Estimators With Different Convergence Rates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1463-1478, December.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1463-1478
    DOI: 10.1080/01621459.2014.960966
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    References listed on IDEAS

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    1. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
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    5. Chen, Yi-Hau & Chatterjee, Nilanjan & Carroll, Raymond J., 2009. "Shrinkage Estimators for Robust and Efficient Inference in Haplotype-Based Case-Control Studies," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 220-233.
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    Cited by:

    1. Gildas Mazo & François Portier, 2021. "Parametric versus nonparametric: The fitness coefficient," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1344-1383, December.

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