【摘 要】
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This paper considers the problem of estimating the bounds on the average controlled direct effects (ACDEs) of a treatment variable on an unobserved response var
【机 构】
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Key Laboratory for Applied Statistics of Ministry of Education, School of Mathematics and Statistics
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This paper considers the problem of estimating the bounds on the average controlled direct effects (ACDEs) of a treatment variable on an unobserved response variable in the presence of unobserved confounders between an intermediate variable and the response variable.When the response variable is observed,Cai,et al.(2008) derived the formulas for the sharp bounds on the ACDEs.When the response variable is unobserved,the authors propose a graphical criterion for selecting variables affected by the response variable to derive the formulas for the bounds on the ACDEs,which is an extension of the result of Kuroki(2005) to ACDEs.The results enable us not only to judge from the graph structure whether the bounds on the ACDEs can be expressed through observed variables when the response variable is unobserved,but also to provide their formulas when the answer is affirmative.
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