On average derivative quantile regression

Chaudhuri, Probal; Doksum, Kjell A.; Samarov, Alexander

doi:10.1214/aos/1031833670

Cited by 228 publications

(186 citation statements)

References 35 publications

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“…More recently, nonparametric and semiparametric quantile regression models have attracted a great deal of research attention due to their greater flexibility than tightly specified parametric models. See, for example, Chaudhuri (1991), He and Shi (1996), Chaudhuri, Doksum and Samarov (1997), He, Ng and Portnoy (1998), Yu and Jones (1998), Koenker, Ng and Portnoy (1998), He and Ng (1999), He and Liang (2000), He and Portnoy (2000), Honda (2000Honda ( , 2004, Khindanova and Rachev (2000), Cai (2002a), De Gooijer andGannoun (2003), Kim (2007), Lee (2003), Yu and Lu (2004), Horowitz and Lee (2005), Cai and Xu (2008), Cai, Gu and Li (2009) and references therein for recent statistics and econometrics literature.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

Cai

Zhang

2012

Journal of Econometrics

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We study quantile regression estimation for dynamic models with partially varying coefficients so that the values of some coefficients may be functions of informative covariates.Estimation of both parametric and nonparametric functional coefficients are proposed.In particular, we propose a three stage semiparametric procedure. Both consistency and asymptotic normality of the proposed estimators are derived. We demonstrate that the parametric estimators are root-n consistent and the estimation of the functional coefficients is oracle. In addition, efficiency of parameter estimation is discussed and a simple efficient estimator is proposed. A simple and easily implemented test for the hypothesis of varying-coefficient is proposed. A Monte Carlo experiment is conducted to evaluate the performance of the proposed estimators.KEY WORDS: Efficiency; nonlinear time series; partially linear; partially varying coefficients; quantile regression; semiparametric. * We thank two referees and the guest Editors for their very helpful comments and suggestions. We also thank the audiences at the

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Section: Introductionmentioning

confidence: 99%

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

Cai

Zhang

2012

Journal of Econometrics

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“…An approach that circumvents this problem is measuring the average marginal response of the covariates on the CQF directly. The average quantile derivative, defined as E[W(X)∇Q τ (Y|X)] where W(X) is a weight function, offers such a succinct summary statistic ( [27]). Sasaki [28] investigates the question that quantile regressions may misspecify true structural functions.…”

Section: Linear Regression Modelmentioning

confidence: 99%

Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification

Lee

2015

Econometrics

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Allowing for misspecification in the linear conditional quantile function, this paper provides a new interpretation and the semiparametric efficiency bound for the quantile regression parameter β(τ) in Koenker and Bassett (1978). The first result on interpretation shows that under a mean-squared loss function, the probability limit of the Koenker-Bassett estimator minimizes a weighted distribution approximation error, defined as F Y (X β(τ)|X) − τ, i.e., the deviation of the conditional distribution function, evaluated at the linear quantile approximation, from the quantile level. The second result implies that the Koenker-Bassett estimator semiparametrically efficiently estimates the quantile regression parameter that produces parsimonious descriptive statistics for the conditional distribution. Therefore, quantile regression shares the attractive features of ordinary least squares: interpretability and semiparametric efficiency under misspecification.

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“…Nonparametric estimation of the conditional median function has proven useful in the estimation of several semiparametric models: see, for example Chaudhuri et al (1997), Khan (2001), Chen and Khan (1998a, b, 2000, 2001. In the context of this model, an equivariance property of quantiles implies that the conditional quantile function, denoted q (·), is of the form…”

Section: Local Linear Estimation Of the Conditional Quantile Functionmentioning

confidence: 99%

“…We ÿrst 'plug in' the local Bahadur representation for the local linear estimator established in Chaudhuri (1991a), Chaudhuri et al (1997). Following the same steps used in the proof of Lemma 5 of Chen and Khan (2000), we can express this term as a second order U-statistic plus an asymptotically negligible remainder term: where the second equality follows from Assumption LL2.…”

Section: A2 4th-root Consistencymentioning

confidence: 99%

Two-step estimation of semiparametric censored regression models

Khan

Powell

2001

Journal of Econometrics

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Root-n-consistent estimators of the regression coe cients in the linear censored regression model under conditional quantile restrictions on the error terms were proposed by Powell (Journal of Econometrics 25 (1984) 303-325, 32 (1986a. While those estimators have desirable asymptotic properties under weak regularity conditions, simulation studies have shown these estimators to exhibit a small sample bias in the opposite direction of the least squares bias for censored data. This paper introduces two-step estimators for these models which minimize convex objective functions, and are designed to overcome this ÿnite-sample bias. The paper gives regularity conditions under which the proposed two-step estimators are consistent and asymptotically normal; a Monte Carlo study compares the ÿnite sample behavior of the proposed methods with their one-step counterparts. ? 2001 Elsevier Science S.A. All rights reserved.

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On average derivative quantile regression

Cited by 228 publications

References 35 publications

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification

Two-step estimation of semiparametric censored regression models

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