Extremal linear quantile regression with Weibull-type tails

Abstract

This paper studies the estimation of extreme conditional quantiles for distributions with Weibull-type tails. We propose two families of estimators for the Weibull tail-coefficient, and construct an extrapolation estimator for the extreme conditional quantiles based on quantile regression and extreme value theory. The asymptotic results of the proposed estimators are established. The work fills a gap in the literature of extreme quantile regression where many important Weibull-type distributions are excluded by the assumed strong conditions. We demonstrate through simulation study that the proposed Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing) Extremal linear quantile regression with Weibull-type tails extrapolation method provides more efficient and stable estimation of conditional quantiles of extreme orders than the conventional method.The practical value of the proposed method is demonstrated through the analysis of extremely high birth weight.

A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

“…Moreover, measures such as the Cook distance and generalized leverage are essential diagnostic aspects of all statistical modeling, and they must be further studied for the newly proposed model. Weibull-type distributions with an extreme value index are widely used in many areas such as environmental sciences, hydrology, and meteorology; see [42]. Our proposed methodology can be adapted to this type of distributions.…”

Parametric modal regression with error in covariates

“…It has also been well understood that ignoring covariates measurement error in mean regression or quantile regression usually lead to misleading inference results. There exists a large collection of works on mean regression methodology accounting for measurement error (Buonaccorsi, 2010;Carroll et al, 2006;Fuller, 2009;Yi, 2017), and also some works in quantile regression to address this complication (He & Liang, 2000;Wang et al, 2012;Wei & Carroll, 2009). Modal regression methodology that address this issue only emerged recently, including those developed by Zhou and Huang (2016), Li and Huang (2019), and Shi et al (2021), all of which opted for a nonparametric model for the error term in the primary regression model.…”

Quantile regression with multiple proxy variables

“…Specifically, we consider the problem of estimating the quantile function in the presence of multiple proxies for true covariates. As in conventional linear regression, the quantile regression estimator's inconsistency in the absence of a true covariate is a commonly discussed issue in the literature (Brown, 1982; Carroll et al, 2006; He & Liang, 2000; Hausman et al, 2021; Montes‐Rojas, 2011; Wei & Carroll, 2009).…”

“…Several studies have incorporated proxy variables in quantile regression estimation. He and Liang (2000)—considering the problem of estimating quantile regression coefficients in errors‐in‐variables models with a proxy variable—proposed an estimator in the context of linear and partially linear models. Wei and Carroll (2009) presented a nonparametric method for correcting bias caused by measurement error in the linear quantile regression model by constructing joint estimating equations that simultaneously hold for all quantile levels.…”