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Quantile regression with interval data

Arie Beresteanu and Yuya Sasaki

Econometric Reviews, 2021, vol. 40, issue 6, 562-583

Abstract: This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for regular random variables. We then give sharp characterization of this set by extending concepts from random set theory. Applying the identification set of quantiles and its sharpness to parametric quantile regression models yields the identification set of the parameters and its sharpness. We apply our methods to data on localized environmental benefits and their impact on house values.

Date: 2021
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DOI: 10.1080/07474938.2021.1889201

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