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Activity Number: 184 - SPEED: Variable Selection and Networks
Type: Contributed
Date/Time: Monday, July 31, 2017 : 11:35 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #325377
Title: Detection of Treatment Effect After Variable Selection Under Model Misspecification
Author(s): Jingshen Wang* and Xuming He
Companies: University of Michigan and University of Michigan
Keywords: post selection inference ; treatment effect ; model misspecification ; multiple data splitting ; p-value aggregation ; hypothesis test
Abstract:

Detection of treatment effect is frequently needed in treatment or policy evaluations. We consider the problem of treatment effect detection in the context of model selection when a large number of covariates are present and there are possible violations of the assumed link function, which is the functional form of the model which relates the outcome variable to the covariates and the random error. We allow the true link function to be completely arbitrary expect that y depends on covariates only though a linear combination of x. Under certain assumptions, the Lasso-type method under model misspecification is shown to have the sure screening property. However, it is generally invalid to perform data-driven model selection and derive statistical inference from the selected model. We adopt the idea of data splitting, where the number of variables is then reduced to a manageable size using the first split, while classical testing method under model misspecification can be applied to the remaining variables, using the data from the second split. Multiple random split is performed to reproduce the result and tame the erratic discontinuities of selection-based estimators.


Authors who are presenting talks have a * after their name.

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