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September 2009 Error-free milestones in error prone measurements
Dylan S. Small, Paul R. Rosenbaum
Ann. Appl. Stat. 3(3): 881-901 (September 2009). DOI: 10.1214/08-AOAS233


A predictor variable or dose that is measured with substantial error may possess an error-free milestone, such that it is known with negligible error whether the value of the variable is to the left or right of the milestone. Such a milestone provides a basis for estimating a linear relationship between the true but unknown value of the error-free predictor and an outcome, because the milestone creates a strong and valid instrumental variable. The inferences are nonparametric and robust, and in the simplest cases, they are exact and distribution free. We also consider multiple milestones for a single predictor and milestones for several predictors whose partial slopes are estimated simultaneously. Examples are drawn from the Wisconsin Longitudinal Study, in which a BA degree acts as a milestone for sixteen years of education, and the binary indicator of military service acts as a milestone for years of service.


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Dylan S. Small. Paul R. Rosenbaum. "Error-free milestones in error prone measurements." Ann. Appl. Stat. 3 (3) 881 - 901, September 2009.


Published: September 2009
First available in Project Euclid: 5 October 2009

zbMATH: 1196.62048
MathSciNet: MR2750218
Digital Object Identifier: 10.1214/08-AOAS233

Keywords: Attenuation , errors in measurement , Full matching , instrumental variables , nonbipartite matching , questionnaire design

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.3 • No. 3 • September 2009
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