Data enriched linear regression

Citations Over TimeTop 12% of 2015 papers

Abstract

We present a linear regression method for predictions on a small data set making use of a second possibly biased data set that may be much larger. Our method fits linear regressions to the two data sets while penalizing the difference between predictions made by those two models. The resulting algorithm is a shrinkage method similar to those used in small area estimation. We find a Stein-type result for Gaussian responses: when the model has $5$ or more coefficients and $10$ or more error degrees of freedom, it becomes inadmissible to use only the small data set, no matter how large the bias is. We also present both plug-in and AICc-based methods to tune our penalty parameter. Most of our results use an $L_{2}$ penalty, but we obtain formulas for $L_{1}$ penalized estimates when the model is specialized to the location setting. Ordinary Stein shrinkage provides an inadmissibility result for only $3$ or more coefficients, but we find that our shrinkage method typically produces much lower squared errors in as few as $5$ or $10$ dimensions when the bias is small and essentially equivalent squared errors when the bias is large.

Related Papers

• → Influence of shrinkage-reducing agent and polypropylene fiber on shrinkage of ceramsite concrete(2017)77 cited
• Autogenous Shrinkage of Concrete and Its Research Progress(2000)
• The causes and control of shrinkage cracks of concrete(2003)
• Autogenous shrinkage and drying shrinkage of cement paste at early aging(2007)
• Shrinkage Properties of High Performance Concrete with Shrinkage Reducing Agent(2005)