Asymptotic Theory for Nonlinear Quantile Regression Under Weak Dependence

Oberhofer, Walter; Haupt, Harald

doi:10.1017/s0266466615000031

Cited by 15 publications

(13 citation statements)

References 69 publications

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“…Similarly, there exist a variety of approaches to deal with repeated measurements as briefly summarized in our introductory remarks. In Sections 3 and 4, we relied on the consistency of the estimator, which essentially correspond to Karlsson's approach with uniform weights. This is linked to a marginal modeling approach for repeated measures.…”

Section: Methodsmentioning

confidence: 99%

“…Ignoring dependency is nonetheless a successful strategy . This strategy is linked to marginal modeling and leads to a consistent estimator under quite general assumptions . Copula models have also been used in QR modeling with time‐to‐event data …”

Section: Introductionmentioning

confidence: 99%

“…24 This strategy is linked to marginal modeling 37 and leads to a consistent estimator under quite general assumptions. 38,39 Copula models have also been used in QR modeling with time-to-event data. 23,25 In summary, we develop an approach to QR to model time-to-transition following a first-jump representation of the data, via censored QR.…”

Section: Introductionmentioning

confidence: 99%

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Multistate quantile regression models

Farcomeni

Geraci

2019

Statistics in Medicine

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We develop regression methods for inference on conditional quantiles of time‐to‐transition in multistate processes. Special cases include survival, recurrent event, semicompeting, and competing risk data. We use an ad hoc representation of the underlying stochastic process, in conjunction with methods for censored quantile regression. In a simulation study, we demonstrate that the proposed approach has a superior finite sample performance over simple methods for censored quantile regression, which naively assume independence between states, and over methods for competing risks, even when the latter are applied to competing risk data settings. We apply our approach to data on hospital‐acquired infections in cirrhotic patients, showing a quantile‐dependent effect of catheterization on time to infection.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multistate quantile regression models

Farcomeni

Geraci

2019

Statistics in Medicine

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“…An approach based on copulas is developed by Chen, Koenker and Xiao (2009). Oberhofer and Haupt (2016) established the consistency of the L 1 -norm nonlinear quantile estimator under weak dependency. Finally, Geraci (2017a) extended Geraci and Bottai's (2014) quantile mixed models to the nonlinear case.…”

Section: Nonlinear Parametric Modelsmentioning

confidence: 99%

Additive Quantile Regression for Clustered Data with an Application to Children's Physical Activity

Geraci

2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary Additive models are flexible regression tools that handle linear as well as non‐linear terms. The latter are typically modelled via smoothing splines. Additive mixed models extend additive models to include random terms when the data are sampled according to cluster designs (e.g. longitudinal). These models find applications in the study of phenomena like growth, certain disease mechanisms and energy expenditure in humans, when repeated measurements are available. We propose a novel additive mixed model for quantile regression. Our methods are motivated by an application to physical activity based on a data set with more than half a million accelerometer measurements in children of the UK Millennium Cohort Study. In a simulation study, we assess the proposed methods against existing alternatives.

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“…Even if only one observed variable is endogenous, this restriction limits the use of interactions and transformations (like poly-4 Heavy tails in consumption data have been documented recently by Walsh (2015, 2017). 5 For nonlinear QR (no IV), see Powell (1994, §2.2), Oberhofer and Haupt (2016), and references therein. 6 Chernozhukov et al (2017) comment, "This approach bypasses the need to optimize a non-convex and non-smooth criterion at the cost of needing to design a sampler that adequately explores the quasi-posterior in a reasonable amount of computation time."…”

Section: Introductionmentioning

confidence: 99%

Smoothed GMM for quantile models

Castro

Galvao

Kaplan

et al. 2019

Journal of Econometrics

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This paper develops theory for feasible estimators of finite-dimensional parameters identified by general conditional quantile restrictions, under much weaker assumptions than previously seen in the literature. This includes instrumental variables nonlinear quantile regression as a special case. More specifically, we consider a set of unconditional moments implied by the conditional quantile restrictions, providing conditions for local identification. Since estimators based on the sample moments are generally impossible to compute numerically in practice, we study feasible estimators based on smoothed sample moments. We propose a method of moments estimator for exactly identified models, as well as a generalized method of moments estimator for over-identified models. We establish consistency and asymptotic normality of both estimators under general conditions that allow for weakly dependent data and nonlinear structural models. Simulations illustrate the finite-sample properties of the methods. Our in-depth empirical application concerns the consumption Euler equation derived from quantile utility maximization. Advantages of the quantile Euler equation include robustness to fat tails, decoupling of risk attitude from the elasticity of intertemporal substitution, and log-linearization without any approximation error. For the four countries we examine, the quantile estimates of discount factor and elasticity of intertemporal substitution are economically reasonable for a range of quantiles above the median, even when two-stage least squares estimates are not reasonable.

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Asymptotic Theory for Nonlinear Quantile Regression Under Weak Dependence

Cited by 15 publications

References 69 publications

Multistate quantile regression models

Multistate quantile regression models

Additive Quantile Regression for Clustered Data with an Application to Children's Physical Activity

Smoothed GMM for quantile models

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