Extremal quantile treatment effects

Zhang, Yichong

doi:10.1214/17-aos1673

Cited by 23 publications

(34 citation statements)

References 55 publications

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“…To be more specific, there exists

γ > 0

such that

\lim_{t \to \infty} \frac{Q_{ε} ((), 1 prefix- \frac{1}{t u})}{Q_{ε} ((), 1 prefix- \frac{1}{t})} = u^{γ}

for any u > 0. The real‐valued parameter

γ

is referred to as the extreme value index (de Haan & Ferreira, 2006; Gomes & Guillou, 2015; Zhang, 2018). It is important to note that Equation () implies that the conditional distribution of the response Y given Z and X also has a heavy right tail with the same extreme value index

γ

.…”

Section: Estimation Methodsmentioning

confidence: 99%

Extreme quantile estimation for partial functional linear regression models with heavy‐tailed distributions

Zhu

Liu

et al. 2021

Can J Statistics

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In this article, we propose a novel estimator of extreme conditional quantiles in partial functional linear regression models with heavy‐tailed distributions. The conventional quantile regression estimators are often unstable at the extreme tails due to data sparsity, especially for heavy‐tailed distributions. We first estimate the slope function and the partially linear coefficient using a functional quantile regression based on functional principal component analysis, which is a robust alternative to the ordinary least squares regression. The extreme conditional quantiles are then estimated by using a new extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator and illustrate its finite sample performance by simulation studies and an empirical analysis of diffusion tensor imaging data from a cognitive disorder study.

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“…To be more specific, there exists

γ > 0

such that

\lim_{t \to \infty} \frac{Q_{ε} ((), 1 prefix- \frac{1}{t u})}{Q_{ε} ((), 1 prefix- \frac{1}{t})} = u^{γ}

for any u > 0. The real‐valued parameter

γ

γ

.…”

Section: Estimation Methodsmentioning

confidence: 99%

Extreme quantile estimation for partial functional linear regression models with heavy‐tailed distributions

Zhu

Liu

et al. 2021

Can J Statistics

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“…The propensity score Π(x) is generally unknown in practice and needs to be estimated. In this paper, we follow Hirano et al (2003), Firpo (2007) and Zhang (2018) to use the sieve method, a nonparametric regression method, for the estimation of the propensity score. Suppose that we observe n independent copies (Y i , D i , X i ) n i=1 of (Y, D, X).…”

Section: Propensity Score Estimationmentioning

confidence: 99%

“…The asymptotic results for fixed τ in Firpo (2007) no longer hold in this framework. Zhang (2018) established the asymptotic theory for the estimator proposed by Firpo (2007) with changing levels τ n . In particular, he distinguished between the intermediate τ n -QTE where nτ n → ∞ and the moderately extreme τ n -QTE where nτ n → d > 0; note that nτ n is the expected number of observations below the τ n -quantile in a sample of size n. In the intermediate case, he showed that the estimator is asymptotically normal and suggested a valid full-sample bootstrap confidence interval to quantify the uncertainty.…”

Section: Introductionmentioning

confidence: 99%

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Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions

Deuber¹,

Li²,

Engelke³

et al. 2021

Preprint

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Causal inference for extreme events has many potential applications in fields such as medicine, climate science and finance. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximations and uses a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators even in the setting of extremal quantiles, and we propose a consistent variance estimator to achieve valid statistical inference. In simulation studies we illustrate the advantages of our methodology over competitors, and we apply it to a real data set.

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“…They applied this approach to the estimation of the black wage gap for young males in the US. Zhang (2015) employed extremal quantile regression methods to estimate tail quantile treatment effects under a selection on observables assumption. Notation: The symbol → d denotes convergence in law.…”

Section: Introductionmentioning

confidence: 99%

Extremal quantile regression: an overview

Chernozhukov¹,

Fernández‐Val²,

Kaji³

2017

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Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants of low infant birth weights, and auction models. This chapter provides an overview of recent developments in the theory and empirics of extremal quantile regression. The advances in the theory have relied on the use of extreme value approximations to the law of the Koenker and Bassett (1978) quantile regression estimator. Extreme value laws not only have been shown to provide more accurate approximations than Gaussian laws at the tails, but also have served as the basis to develop bias corrected estimators and inference methods using simulation and suitable variations of bootstrap and subsampling. The applicability of these methods is illustrated with two empirical examples on conditional value-at-risk and financial contagion.

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Extremal quantile treatment effects

Cited by 23 publications

References 55 publications

Extreme quantile estimation for partial functional linear regression models with heavy‐tailed distributions

Extreme quantile estimation for partial functional linear regression models with heavy‐tailed distributions

Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions

Extremal quantile regression: an overview

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