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A Simple and Adaptive Confidence Interval when Nuisance Parameters Satisfy an Inequality

Gregory Fletcher Cox

arXiv 16 Sep 2024 · Econometrics

arXiv:2409.09962 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Inequalities may appear in many models. They can be as simple as assuming a parameter is nonnegative, possibly a regression coefficient or a treatment effect. This paper focuses on the case that there is only one inequality and proposes a confidence interval that is particularly attractive, called the inequality-imposed confidence interval (IICI). The IICI is simple. It does not require simulations or tuning parameters. The IICI is adaptive. It reduces to the usual confidence interval (calculated by adding and subtracting the standard error times the $1 - \alpha/2$ standard normal quantile) when the inequality is sufficiently slack. When the inequality is sufficiently violated, the IICI reduces to an equality-imposed confidence interval (the usual confidence interval for the submodel where the inequality holds with equality). Also, the IICI is uniformly valid and has (weakly) shorter length than the usual confidence interval; it is never longer. The first empirical application considers a linear regression when a coefficient is known to be nonpositive. A second empirical application considers an instrumental variables regression when the endogeneity of a regressor is known to be nonnegative.

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57
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Ketz, P (2018) Subvector inference when the true parameter vector may be near or at the boundary1.00063100%
2Elliott, G., Müller, U., and Watson, M (2015) Nearly optimal tests when a nuisance parameter is present under the null hypothesis0.87462100%
3Fan, Y. and Shi, X (2023) Wald, QLR, and score tests when parameters are subject to linear inequality constraints0.81142100%
4Moon, H. and Schorfheide, F (2009) Estimation with overidentifying inequality moment conditions0.81142100%
5Andrews, D. and Guggenberger, P (2010) Asymptotic size and a problem with subsampling and with the m out of n bootstrap0.73732100%
6Cavaliere, G., Nielsen, H., Pedersen, R., and Rahbek, A (2022) Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models0.73732100%
7Ketz, P. and McCloskey, A (2023) Short and simple confidence intervals when the directions of some effects are known0.73732100%
8Blattman, C., Jamison, J., and Sheridan, M (2017) Reducing crime and violence: Experimental evidence from cognitive behavioral therapy in Liberia0.64422100%
9Müller, U. and Norets, A (2016) Credibility of confidence sets in nonstandard econometric problems0.64422100%
10Shapiro, J (2021) The environmental bias of trade policy0.64422100%

Showing the top 10 of 57 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Numerical Analysis of Test Optimality0.974133
2On the Lower Confidence Band for the Optimal Welfare in Policy Learning0.40511