The Annals of Statistics

Extremal quantile treatment effects

Yichong Zhang

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Abstract

This paper establishes an asymptotic theory and inference method for quantile treatment effect estimators when the quantile index is close to or equal to zero. Such quantile treatment effects are of interest in many applications, such as the effect of maternal smoking on an infant’s adverse birth outcomes. When the quantile index is close to zero, the sparsity of data jeopardizes conventional asymptotic theory and bootstrap inference. When the quantile index is zero, there are no existing inference methods directly applicable in the treatment effect context. This paper addresses both of these issues by proposing new inference methods that are shown to be asymptotically valid as well as having adequate finite sample properties.

Article information

Source
Ann. Statist., Volume 46, Number 6B (2018), 3707-3740.

Dates
Received: February 2017
Revised: November 2017
First available in Project Euclid: 11 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.aos/1536631288

Digital Object Identifier
doi:10.1214/17-AOS1673

Mathematical Reviews number (MathSciNet)
MR3852666

Zentralblatt MATH identifier
06965702

Subjects
Primary: 62E20: Asymptotic distribution theory 62G32: Statistics of extreme values; tail inference
Secondary: 62P20: Applications to economics [See also 91Bxx]

Keywords
Extreme quantile intermediate quantile

Citation

Zhang, Yichong. Extremal quantile treatment effects. Ann. Statist. 46 (2018), no. 6B, 3707--3740. doi:10.1214/17-AOS1673. https://projecteuclid.org/euclid.aos/1536631288


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Supplemental materials

  • Supplement to “Extremal quantile treatment effects”. This supplement contains all the proofs, two empirical applications, and simulation results.