arXiv 21 Aug 2017 · Mathematics — Statistics Theory
arXiv:1708.06436 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Baranchik, A. J (1973) Inadmissibility of Maximum Likelihood Estimators in Some Multiple Regression Problems with Three or More Independent Variables | 0.585 | 3 | 1 | 100% |
| 2 | James, W. and Stein, C (1961) Estimation with quadratic loss | 0.585 | 3 | 1 | 100% |
| 3 | Chamberlain, G. and Moreira, M. J (2009) Decision Theory Applied to a Linear Panel Data Model | 0.405 | 1 | 1 | 100% |
| 4 | Hansen, B. E (2007) Least Squares Model Averaging | 0.405 | 1 | 1 | 100% |
| 5 | Hansen, B. E (2016) Efficient shrinkage in parametric models | 0.405 | 1 | 1 | 100% |
| 6 | Spiess, J (2017) Bias Reduction in Instrumental Variable Estimation through First-Stage Shrinkage self | 0.405 | 1 | 1 | 100% |
| 7 | Sclove, S. L (1968) Improved estimators for coefficients in linear regression | 0.405 | 1 | 1 | 100% |
Showing the top 7 of 7 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Bias Reduction in Instrumental Variable Estimation through First-Stage Shrinkage | 0.405 | 1 | 1 |