Inference After Multiple Hypothesis Testing
Researchers often use the same data to choose parameters of interest and make statistical inference on them. However, under such “double dipping” conventional confidence intervals are unreliable. We develop selective inference procedures that are valid conditional on the parameters selected by multiple hypothesis testing methods such as the Holm step-down method.
Confidence sets that have appropriate conditional coverage are constructed for both marginal and joint inference, and conditional median unbiased estimator is proposed. We also discuss how to combine the selective and conventional procedures to offer further performance gains.
Then, we apply our novel procedures to study the effects of a matching grant using data from Karlan and List (2007), and find that the conditional point estimates and confidence intervals can be very different from the conventional ones. In particular, for the application with multiple outcomes, the lower bounds obtained from our procedures are remarkably higher, suggesting an upward correction to the effects.
(Joint work with Andreas Dzemski and Wenjie Wang)
About Ryo Okui
Ryo Okui is an Associate Professor of Economics at Seoul National University. Prior to joining Seoul National University, he was an Associate professor at NYU Shanghai and Kyoto University, and was an Assistant Professor at Hong Kong University of Science and Technology. He was also a Visiting Professor at the University of Gothenburg and a Visiting Associate Professor at Vrije Universiteit Amsterdam. He holds a PhD from the University of Pennsylvania and a Bachelor in Economics from Kyoto University.
His work has appeared in Econometrica, Review of Economic Studies, Journal of Econometrics among other outlets. Professor Okui is a recipient of Ogawa Research Prize from the Japan Statistical Society. He is an associate editor of Japanese Economic Review and the Japanese Journal of Statistics and Data Science. Research Interests: econometrics, experimental economics
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