Simultaneous estimation of quantile curves using quantile sheets

Schnabel, Sabine; Eilers, Paul H.C.

doi:10.1007/s10182-012-0198-1

Cited by 48 publications

(58 citation statements)

References 19 publications

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“…Estimating the complete conditional quantile function is less straightforward since we have to fit separate models for a grid of probabilities τ , and the resulting regression quantiles may cross. Solutions to this problem can be obtained by combining all quantile fits in one joint model based on, for example, location-scale models (He 1997) or quantile sheets (Schnabel and Eilers 2012), or by monotonising the estimated quantile curves using non-decreasing rearrangements (Dette and Volgushev 2008).…”

Section: Introductionmentioning

confidence: 99%

Conditional Transformation Models

Hothorn

Kneib

Bühlmann

2013

Journal of the Royal Statistical Society Series B: Statistical Methodology

100

143

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The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only estimate the conditional mean as a function of the explanatory variables and assume that higher moments are not affected by the regressors. The underlying reason for such a restriction is the assumption of additivity of signal and noise. We propose to relax this common assumption in the framework of transformation models. The novel class of semiparametric regression models proposed herein allows transformation functions to depend on explanatory variables. These transformation functions are estimated by regularised optimisation of scoring rules for probabilistic forecasts, e.g. the continuous ranked probability score. The corresponding estimated conditional distribution functions are consistent. Conditional transformation models are potentially useful for describing possible heteroscedasticity, comparing spatially varying distributions, identifying extreme events, deriving prediction intervals and selecting variables beyond mean regression effects. An empirical investigation based on a heteroscedastic varying coefficient simulation model demonstrates that semiparametric estimation of conditional distribution functions can be more beneficial than kernel-based non-parametric approaches or parametric generalised additive models for location, scale and shape.

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Section: Introductionmentioning

confidence: 99%

Conditional Transformation Models

Hothorn

Kneib

Bühlmann

2013

Journal of the Royal Statistical Society Series B: Statistical Methodology

100

143

View full text Add to dashboard Cite

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“…The idea is based on the paper of Schnabel and Eilers (2013a), on univariate nonparametric quantile regression. The basic idea of their method is to consider a bivariate surface representing the behaviour of the quantile curve in both the covariate and the quantile order τ .…”

Section: Quantile Sheet Methodsmentioning

confidence: 99%

“…The latter is done by adding a specific penalty. We adapt this method to the context of varying-coefficient models, and refer to it as quantile sheet (following the terminology of Schnabel and Eilers (2013a)). …”

Section: Quantile Sheet Methodsmentioning

confidence: 99%

“…Zou and Yuan (2008), Bondell et al (2010), Guo et al (2012), Schnabel and Eilers (2013a), among others, take W h = 1, for all τ h -values, which corresponds with the approach in (3.2). Alexander et al (2011) considers also constant weights W h = 1/H, whereas a fixed weighting scheme assigning the highest weight W h for median estimation is opted for in Koenker (2004) and Lamarche (2010), among others.…”

Section: (Ps)mentioning

confidence: 99%

See 1 more Smart Citation

Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity

2016

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Quantile regression is an important tool for describing the characteristics of conditional distributions. Population conditional quantile functions cannot cross for different quantile orders. Unfortunately estimated regression quantile curves often violate this and cross each other, which can be very annoying for interpretations and further analysis. In this paper we are concerned with flexible varying-coefficient modelling, and develop methods for quantile regression that ensure that the estimated quantile curves do not cross. A second aim of the paper is to allow for some heteroscedasticity in the error modelling, and to also estimate the associated variability function. We investigate the finite-sample performances of the discussed methods via simulation studies. Some applications to real data illustrate the use of the methods in practical settings.

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“…Expectile and quantile sheets are explained in more detail by Schnabel (2011) or Schnabel andEilers (2013).…”

Section: Let F (Y) Be a Cumulative Distribution Function Of Y And G(y)mentioning

confidence: 99%