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Non‐standard rates of convergence of criterion‐function‐based set estimators for binary response models

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  • Jason R. Blevins
Abstract
This paper establishes consistency and non‐standard rates of convergence for set estimators based on contour sets of criterion functions for a semi‐parametric binary response model under a conditional median restriction. The model can be partially identified due to potentially limited‐support regressors and an unknown distribution of errors. A set estimator analogous to the maximum score estimator is essentially cube‐root consistent for the identified set when a continuous but possibly bounded regressor is present. Arbitrarily fast convergence occurs when all regressors are discrete. We also establish the validity of a subsampling procedure for constructing confidence sets for the identified set. As a technical contribution, we provide more convenient sufficient conditions on the underlying empirical processes for cube‐root convergence and a sufficient condition for arbitrarily fast convergence, both of which can be applied to other models. Finally, we carry out a series of Monte Carlo experiments, which verify our theoretical findings and shed light on the finite‐sample performance of the proposed procedures.

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  • Jason R. Blevins, 2015. "Non‐standard rates of convergence of criterion‐function‐based set estimators for binary response models," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 172-199, June.
    • Handle: RePEc:wly:emjrnl:v:18:y:2015:i:2:p:172-199
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    File URL: http://hdl.handle.net/10.1111/ectj.12048
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    Cited by:

    1. Adam M. Rosen & Takuya Ura, 2019. "Finite Sample Inference for the Maximum Score Estimand," Papers 1903.01511, arXiv.org, revised May 2020.

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