Error-free milestones in error prone measurements

Details Error-free milestones in error prone measurements Error-free milestones in error prone measurements

2009-10-07

arxiv.org/abs/0910.1233v1

Annals of Applied Statistics 2009, Vol. 3, No. 3, 881-901

Statistics

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Published in at http://dx.doi.org/10.1214/08-AOAS233 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

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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