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Unbiased Shrinkage Estimation

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  • Jann Spiess

Abstract

Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of covariates. In a linear regression model with homoscedastic Normal noise, I consider shrinkage estimation of the nuisance parameters associated with control variables. For at least three control variables and exogenous treatment, I establish that the standard least-squares estimator is dominated with respect to squared-error loss in the treatment effect even among unbiased estimators and even when the target parameter is low-dimensional. I construct the dominating estimator by a variant of James-Stein shrinkage in a high-dimensional Normal-means problem. It can be interpreted as an invariant generalized Bayes estimator with an uninformative (improper) Jeffreys prior in the target parameter.

Suggested Citation

  • Jann Spiess, 2017. "Unbiased Shrinkage Estimation," Papers 1708.06436, arXiv.org, revised Oct 2017.
  • Handle: RePEc:arx:papers:1708.06436
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    File URL: http://arxiv.org/pdf/1708.06436
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    References listed on IDEAS

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    1. Gary Chamberlain & Marcelo J. Moreira, 2009. "Decision Theory Applied to a Linear Panel Data Model," Econometrica, Econometric Society, vol. 77(1), pages 107-133, January.
    2. Hansen, Bruce E., 2016. "Efficient shrinkage in parametric models," Journal of Econometrics, Elsevier, vol. 190(1), pages 115-132.
    3. Jann Spiess, 2017. "Bias Reduction in Instrumental Variable Estimation through First-Stage Shrinkage," Papers 1708.06443, arXiv.org, revised Oct 2017.
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