文章基本信息

标题：Data enriched linear regression
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作者：Aiyou Chen ; Art B. Owen ; Minghui Shi 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2015
卷号：9
期号：1
页码：1078-1112
DOI：10.1214/15-EJS1027
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Data fusion;small area estimation;Stein shrink age;transfer learning.