Optimal inference in a class of regression models

By T. Armstrong, Michael J. Kolesar. 2015

148 citations recorded by the source corpus.

We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is not known. When the function class is centrosymmetric, these efficiency bounds imply that minimax CIs are close to efficient at smooth regression functions. This implies, in particular, that it is impossible to form CIs that are tighter using data-dependent tuning parameters, and maintain coverage over the whole function class. We specialize our results to inference on the regression discontinuity parameter, and illustrate them in simulations and an empirical application.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/90262601fe457ed7c6bbf52594d3a8cedc3dcd24

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Citations in the corpus

Testing continuity of a density via g-order statistics in the regression discontinuity design (2018, methodology): “One could alternatively replace the normality assumption with a non-parametric estimator of fZ(z̄) but it is unfortunately impossible to choose CP adaptively for testing (3) (see, e.g., Low, 1997; Armstrong and Kolesár, 2018).”
Sensitivity analysis using approximate moment condition models (2018, methodology): “3 of Armstrong and Kolesár (2018). The universal lower bound for κ∗ follows from the following result:”
Local Projection Inference Is Simpler and More Robust Than You Think (2020, methodology): “…possibility is to impose a priori bounds on the rate of decay of the VAR coefficients, and then take the resulting worst-case bias of finite-p local projection estimators into account when constructing confidence intervals (as in the “honest inference” approach of Armstrong and Kolesar, 2018).”
Augmented minimax linear estimation (2017, background): “Donoho (1994) and related papers (Armstrong and Kolesár, 2018; Cai and Low, 2003; Donoho and Liu, 1991; Ibragimov and Khas’minskii, 1985; Johnstone, 2015; Juditsky and Nemirovski, 2009) show that when a regression function m is in a convex set F and Yi ∣∣Zi ∼ N(0, σ(2) i ), a minimax linear estimato”
Factorial Designs, Model Selection, and (Incorrect) Inference in Randomized Experiments (2019, methodology): “20This is because the one-sided long model t-tests are uniformly most powerful (e.g., Proposition 15.2 in van der Vaart, 1998) so that, for any β12, the maximal power is achieved by a one-sided ttest (e.g., Armstrong & Kolesar, 2015, 2021).”
Debiased Inference of Average Partial Effects in Single-Index Models (2018, methodology): “However, a key aspect of both the conditionally linear model (2) and the fully generic model underlying (3) is that the underlying model class for m(·) is convex, and convexity plays a key role in enabling practical inference about linear functionals [Armstrong and Kolesár, 2018, Donoho, 1994, Hirsh”
What’s trending in difference-in-differences? A synthesis of the recent econometrics literature (2022, unknown): “Rambachan and Roth (2022b) use tools from the partial identification and sensitivity analysis literature (Armstrong and Kolesár, 2018; Andrews et al., 2023) to construct confidence sets for the ATT that are uniformly valid under the imposed restrictions.”
On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference (2015, methodology): “For more recent work on bias and related issues in nonparametric inference, seeHall andHorowitz (2013), Calonico, Cattaneo, and Titiunik (2014), Armstrong and Kolesár (2017), Schennach (2015), and references therein. We also contribute to the literature onEdgeworth expansions, which have been used b”