Publications

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Hybrid Confidence Intervals for Informative Uniform Asymptotic Inference After Model Selection, revise and resubmit at Biometrika

I propose a new type of confidence interval for correct asymptotic inference after using data to select a model of interest without assuming any model is correctly specified.  This hybrid confidence interval is constructed by combining techniques from the selective inference and post-selection inference literatures to yield a short confidence interval across a wide range of data realizations.  I show that hybrid confidence intervals have correct asymptotic coverage, uniformly over a large class of probability distributions that do not bound scaled model parameters.  I illustrate the use of these confidence intervals in the problem of inference after using the LASSO objective function to select a regression model of interest and provide evidence of their desirable length and coverage properties in small samples via a set of Monte Carlo experiments that entail a variety of different data distributions as well as an empirical application to the predictors of diabetes disease progression.

Critical Values Robust to P-hacking (with Pascal Michaillat)

(previously titled "Incentive-Compatible Critical Values")

P-hacking occurs when researchers engage in various behaviors that increase their chances of reporting statistically significant results. P-hacking is problematic because it reduces the informativeness of hypothesis tests - by making significant results much more common than they are supposed to be in the absence of true significance. Despite its prevalence, p-hacking is not taken into account in hypothesis testing theory: the critical values used to determine significance assume no p-hacking. To address this problem, we build a model of p-hacking and use it to construct critical values such that, if these values are used to determine significance, and if researchers adjust their behavior to these new significance standards, then significant results occur with the desired frequency. Because such robust critical values allow for p-hacking, they are larger than classical critical values. As an illustration, we calibrate the model with evidence from the social and medical sciences. We find that the robust critical value for any test is the classical critical value for the same test with one fifth of the significance level - a form of Bonferroni correction. For instance, for a z-test with a significance level of 5%, the robust critical value is 2.31 instead of 1.65 if the test is one-sided and 2.57 instead of 1.96 if the test is two-sided.

Inference on Winners (with Isaiah Andrews and Toru Kitagawa), revise and resubmit at Quarterly Journal of Economics

R Code

2019 Version (referenced in "Inference After Estimation of Breaks")

Many empirical questions concern target parameters selected through optimization.  For example, researchers may be interested in the effectiveness of the best policy found in a randomized trial, or the best-performing investment strategy based on historical data.  Such settings give rise to a winner's curse, where conventional estimates are biased and conventional confidence intervals are unreliable.  This paper develops optimal confidence intervals and median-unbiased estimators that are valid conditional on the target selected and so overcome this winner's curse. If one requires validity only on average over targets that might have been selected, we develop hybrid procedures that combine conditional and projection confidence intervals to offer further performance gains relative to existing alternatives.