A location‐scale model for non‐crossing expectile curves

Schnabel, Sabine; Eilers, Paul H.C.

doi:10.1002/sta4.27

Cited by 17 publications

(15 citation statements)

References 33 publications

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“…Note that the calculation of quantiles from expectiles is somewhat numerically demanding. Alternative approaches to estimate quantiles from expectiles are described in Efron (1991) and Schnabel and Eilers (2013a). Schnabel and Eilers (2013a) propose to estimate non-crossing expectile curves using a so-called expectile bundle.…”

Section: Quantiles From Expectilesmentioning

confidence: 99%

“…Alternative approaches to estimate quantiles from expectiles are described in Efron (1991) and Schnabel and Eilers (2013a). Schnabel and Eilers (2013a) propose to estimate non-crossing expectile curves using a so-called expectile bundle. Within the expectile bundle crossing curves are prevented but, as a location scale model is assumed, one also loses flexibility.…”

Section: Quantiles From Expectilesmentioning

confidence: 99%

“…Within the expectile bundle crossing curves are prevented but, as a location scale model is assumed, one also loses flexibility. Schnabel and Eilers (2013a) also give a description of how to estimate the density (and therefore, quantiles) from a set of expectiles by using penalized least squares. The approach by Efron (1991) is a more naive way to get an estimation for quantiles on a bases of expectiles.…”

Section: Quantiles From Expectilesmentioning

confidence: 99%

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Expectile and quantile regression—David and Goliath?

Waltrup

Sobotka

Kneib

et al. 2014

Statistical Modelling

101

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Recent interest in modern regression modelling has focused on extending available (mean) regression models by describing more general properties of the response distribution. An alternative approach is quantile regression where regression effects on the conditional quantile function of the response are assumed. While quantile regression can be seen as a generalization of median regression, expectiles as alternative are a generalized form of mean regression.Generally, quantiles provide a natural interpretation even beyond the 0.5 quantile, the median. A comparable simple interpretation is not available for expectiles beyond the 0.5 expectile, the mean. Nonetheless, expectiles have some interesting properties, some of which are discussed in this article. We contrast the two approaches and show how to get quantiles from a fine grid of expectiles. We compare such quantiles from expectiles with direct quantile estimates regarding efficiency. We also look at regression problems where both quantile and expectile curves have the undesirable property that neighbouring curves may cross each other. We propose a modified method to estimate non-crossing expectile curves based on splines. In an application, we look at the expected shortfall, a risk measure used in finance, which requires both expectiles and quantiles for estimation and which can be calculated easily with the proposed methods in the article.

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Section: Quantiles From Expectilesmentioning

confidence: 99%

Section: Quantiles From Expectilesmentioning

confidence: 99%

Section: Quantiles From Expectilesmentioning

confidence: 99%

See 1 more Smart Citation

Expectile and quantile regression—David and Goliath?

Waltrup

Sobotka

Kneib

et al. 2014

Statistical Modelling

101

View full text Add to dashboard Cite

show abstract

“…On the other hand, we should ignore points close to the boundary or lying outside S m unless the data set include sufficient observation the extreme regions of the design space to allow a reliable computation of quantiles. Schnabel and Eilers (2013a) point out that, although in many cases crossing is only a visual annoyance, it may jeopardize further analysis, e.g., when studying conditional distributions at specific values of the independent variable.…”

Section: Crossing Quantile Regressionsmentioning

confidence: 99%

Quantile Regression Estimation Using Non-Crossing Constraints

Amerise¹

2018

Journal of Mathematics and Statistics

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In this article we are concerned with a collection of multiple linear regressions that enable the researcher to gain an impression of the entire conditional distribution of a response variable given a set of explanatory variables. More specifically, we investigate the advantage of using a new method to estimate a bunch of non-crossing quantile regressions hyperplanes. The main tool is a weighting system of the data elements that aims to reduce the effect of contamination of the sampled population on the estimated parameters by diminishing the effect of outliers. The performances of the new estimators are evaluated on a number of data sets. We had considerable success with avoiding intersections and in the same time improving the global fitting of conditional quantile regressions. We conjecture that in other situations (e.g., data with high level of skewness, non-constant variances, unusual and imputed data) the method of weighted non-crossing quantiles will lead to estimators with good robustness properties.

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“…All the former approaches are based on non-simultaneous estimation, meaning that they use single quantile objective functions. Schnabel and Eilers (2013b) considered a location-scale model for obtaining non-crossing expectile curves.…”

Section: Introductionmentioning

confidence: 99%

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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A location‐scale model for non‐crossing expectile curves

Cited by 17 publications

References 33 publications

Expectile and quantile regression—David and Goliath?

Expectile and quantile regression—David and Goliath?

Quantile Regression Estimation Using Non-Crossing Constraints

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

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