Andrews, D., Cheng, X., and Guggenberger, P. (2020a). Generic results for establishing the asymptotic size of confidence sets and tests. Journal of Econometrics, Forthcoming.
Andrews, I., Kitagawa, T., and McCloskey, A. (2020b). Inference after estimation of breaks. Journal of Econometrics, Forthcoming.
Andrews, I., Roth, J., and Pakes, A. (2019). Inference for linear conditional moment inequalities. Unpublished Manuscript.
Armstrong, T., Kolesar, M., and Plagborg-Moller, M. (2020). Robust empirical bayes confidence intervals. Unpublished Manuscript.
- Bachoc, F., Preinerstorfer, D., and Steinberger, L. (2020). Uniformly valid confidence intervals post-model-selection. Annals of Statistics, 48(1):440â463.
Paper not yet in RePEc: Add citation now
Baird, S., Hicks, J. H., Kremer, M., and Miguel, E. (2016). Worms at work: Longrun impacts of a child health investment. The Quarterly Journal of Economics, 131(4):1637â1680.
Banerjee, A., Hanna, R., Kyle, J., Olken, B. A., and Sumarto, S. (2018). Tangible information and citizen empowerment: Identification cards and food subsidy programs in Indonesia. Journal of Political Economy, 126(2):451â491.
- Bergman, P., Chetty, R., DeLuca, S., Hendren, N., Katz, L. F., and Palmer, C. (2020). Creating moves to opportunity: Experimental evidence on barriers to neighborhood choice. Unpublished Manuscript.
Paper not yet in RePEc: Add citation now
- Berk, R., Brown, L., Buja, A., Zhang, K., and Zhao, L. (2013). Valid post-selection inference. Annals of Statistics, 41(2):802â831.
Paper not yet in RePEc: Add citation now
BjoÌrkman Nyqvist, M. and Jayachandran, S. (2017). Mothers care more, but fathers decide: Educating parents about child health in Uganda. American Economic Review, 107(5):496â500.
- Chakraborty, B. and Murphy, S. (2014). Dynamic treatment regimes. Annual Review of Statistics and Its Applications, 1:447â64.
Paper not yet in RePEc: Add citation now
Chernozhukov, V., Lee, S., and Rosen, A. (2013). Intersection bounds: Estimation and inference. Econometrica, 81(2):667â737.
- Chetty, R. and Hendren, N. (2016a). The impacts of neighborhoods on intergenerational mobility i: Childhood exposure effects. Quarterly Journal of Economics, 133(3):1107â1162.
Paper not yet in RePEc: Add citation now
Chetty, R. and Hendren, N. (2016b). The impacts of neighborhoods on intergenerational mobility ii: County-level estimates. Quarterly Journal of Economics, 133(3):1163â1228.
Chetty, R., Friedman, J., Hendren, N., Jones, M. R., and Porter, S. R. (2018). The opportunity atlas: Mapping the childhood roots of social mobility. Unpublished Manuscript.
- Cox, G. (2018). Almost sure uniqueness of a global minimum without convexity. Annals of Statistics, 48(1):584â606.
Paper not yet in RePEc: Add citation now
- Dawid, A. P. (1994). Selection paradoxes in bayesian inference. Institute of Mathematical Statistics Lecture Notes - Monograph Series, 24:211â220.
Paper not yet in RePEc: Add citation now
Duflo, E., Greenstone, M., Pande, R., and Ryan, N. (2018). The value of regulatory discretion: Estimates from environmental inspections in India. Econometrica, 86(6):2123â2160.
- Eliasz, P. (2004). Optimal median unbiased estimation of coefficients on highly persistent regressors. Unpublished Manuscript.
Paper not yet in RePEc: Add citation now
- Ferguson, J. P., Cho, J. H., Yang, C., and Zhao, H. (2013). Empirical bayes correction for the winnerâs curse in genetic association studies. Genetic Epidemiology, 37(1):60â68.
Paper not yet in RePEc: Add citation now
- Fithian, W., Sun, D., and Taylor, J. (2017). Optimal inference after model selection. arXiv.
Paper not yet in RePEc: Add citation now
- Han, S. (2020). Identification in nonparametric models for dynamic treatment effects. Journal of Econometrics, Forthcoming.
Paper not yet in RePEc: Add citation now
Hansen, P. R. (2005). A test for superior predictive ability. Journal of Business and Economic Statistics, 23(4):365â380.
- Harris, X. T., Panigrahi, S., Markovic, J., Bi, N., and Taylor, J. (2016). Selective sampling after solving a convex problem. arXiv.
Paper not yet in RePEc: Add citation now
Karlan, D. and List, J. A. (2007). Does price matter in charitable giving? evidence from a large-scale natural field experiment. American Economic Review, 97(5):1774â1793.
Khan, A. Q., Khwaja, A. I., and Olken, B. A. (2016). Tax farming redux: Experimental evidence on performance pay for tax collectors. The Quarterly Journal of Economics, 131(1):219â271.
- Kitagawa, T. and Tetenov, A. (2018a). Supplement to âwho should be treated? empirical welfare maximization methods for treatment choiceâ. Econometrica.
Paper not yet in RePEc: Add citation now
Kitagawa, T. and Tetenov, A. (2018b). Who should be treated? empirical welfare maximization methods for treatment choice. Econometrica, 86(2):591â616.
- Kivaranovic, D. and Leeb, H. (2020). On the length of post-model-selection confidence intervals conditional on polyhedral constraints. Journal of the American Statistical Association, Forthcoming.
Paper not yet in RePEc: Add citation now
- Kuchibhotla, A. K., Brown, L. D., Buja, A., Cai, J., George, E. I., and Zhao, L. (2020). Valid post-selection inference in model-free linear regression. Annals of Statistics, Forthcoming.
Paper not yet in RePEc: Add citation now
Laber, E. and Murphy, S. (2011). Adaptive confidence intervals for the test error in classification. Journal of the American Statistical Association, 106(495):904â913.
- Lee, J. D., Sun, D. L., Sun, Y., and Taylor, J. E. (2016). Exact post-selection inference, with application to the LASSO. Annals of Statistics, 44(3):907â927.
Paper not yet in RePEc: Add citation now
- Lee, M. R. and Shen, M. (2018). Winnerâs curse: Bias estimation for total effects of features in online controlled experiments. In KDD.
Paper not yet in RePEc: Add citation now
- Lehmann, E. and ScheffeÌ, H. (1955). Completeness, similar regions, and unbiased estimation: Part ii. SankhyaÌ: The Indian Journal of Statistics, 15(3):219â236.
Paper not yet in RePEc: Add citation now
- Lehmann, E. L. and Romano, J. P. (2005). Testing Statistical Hypotheses. Springer, third edition.
Paper not yet in RePEc: Add citation now
McCloskey, A. (2017). Bonferroni-based size-correction for nonstandard testing problems. Journal of Econometrics, 200(1):17â35.
Mogstad, M., Romano, J. P., Shaikh, A., and Wilhelm, D. (2020). Inference for ranks with applications to mobility across neighborhoods and academic achievement across countries. Unpublished Manuscript.
- Pfanzagl, J. (1979). On optimal median unbiased estimators in the presence of nuisance parameters. Annals of Statistics, 7(1):187â193.
Paper not yet in RePEc: Add citation now
- Pfanzagl, J. (1994). Parametric Statistical Theory. De Gruyter.
Paper not yet in RePEc: Add citation now
- Rai, Y. (2018). Statistical inference for treatment assignment policies. Unpublished Manuscript.
Paper not yet in RePEc: Add citation now
Romano, J. P. and Wolf, M. (2005). Stepwise multiple testing as formalized data snooping.
Romano, J. P., Shaikh, A., and Wolf, M. (2014). A practical two-step method for testing moment inequalities. Econometrica, 82(5):1979â2002.
Tetenov, A. (2012). Statistical treatment choice based on asymmetric minimax regret criteria. Journal of Econometrics, 166(1):157â165.
- Tian, X. and Taylor, J. (2018). Selective inference with a randomized response. Annals of Statistics, 46(2):679â710.
Paper not yet in RePEc: Add citation now
- Tibshirani, R. J., Rinaldo, A., Tibshirani, R., and Wasserman, L. (2018). Uniform asymptotic inference and the bootstrap after model selection. Annals of Statistics, 46(3):1255â1287.
Paper not yet in RePEc: Add citation now
- van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge University Press.
Paper not yet in RePEc: Add citation now
White, H. (2000). A reality check for data snooping. Econometrica, 68(5):1097â1126.
- Y (θÌ)âCSβ P o â¤1. C Alternatives to Conventional Sample Splitting In Section 3.3 of the main text, we discuss the relationship of our conditional approach to conventional sample splitting methods and note that the results of Fithian et al. (2017) imply that traditional sample splitting methods are dominated in our setting. Here, we derive optimal split-sample confidence intervals and estimators as well as easy-to-implement confidence intervals and estimators that dominate their conventional split-sample counterparts in the asymptotic version of the split-sample problem. The Split-Sample Limit Experiment Let Ï denote the fraction of the full sample used to compute the estimated maximum and let (X1 n,Y 1 n ) and (X2 n,Y 2 n ) correspond to the first and second portions of the data, with (X1 n,Y 1 n )=Ïâ1/2 (X[Ïn],Y[Ïn]), (X2 n,Y 2 n )=(1âÏ)â1 (Xn,Yn)â â Ï(X[Ïn]+1,Y[Ïn]+1)
Paper not yet in RePEc: Add citation now
- Zhong, H. and Prentice, R. (2009). Correcting âwinnerâs curseâ in odds ratios from genomewide association findings for major complex human diseases. Genetic Epidemiology, 34(1):78â91.
Paper not yet in RePEc: Add citation now