Geoadditive expectile regression

Sobotka, Fabian; Kneib, Thomas

doi:10.1016/j.csda.2010.11.015

Cited by 118 publications

(93 citation statements)

References 14 publications

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“…They are implicitly defined by μ τ = arg min m E [w i,τ (m, ε i )(ε i,τ − m) 2 ]. Least asymmetrically weighted squares (LAWS) estimation of expectiles dates already back to Newey and Powell (1987) but recently re-gained interest in the context of semiparametric or geoadditive regression (see for example Schnabel and Eilers 2009;Sobotka and Kneib 2010). Expectile estimation is thereby a special form of M-quantile estimation, see Breckling and Chambers (1988), Jones (1994).…”

Section: Expectilesmentioning

confidence: 99%

On confidence intervals for semiparametric expectile regression

et al. 2011

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In regression scenarios there is a growing demand for information on the conditional distribution of the response beyond the mean. In this scenario quantile regression is an established method of tail analysis. It is well understood in terms of asymptotic properties and estimation quality. Another way to look at the tail of a distribution is via expectiles. They provide a valuable alternative since they come with a combination of preferable attributes. The easy weighted least squares estimation of expectiles and the quadratic penalties often used in flexible regression models are natural partners. Also, in a similar way as quantiles can be seen as a generalisation of median regression, expectiles offer a generalisation of mean regression. In addition to regression estimates, confidence intervals are essential for interpretational purposes and to assess the variability of the estimate, but there is a lack of knowledge regarding the asymptotic properties of a semiparametric expectile regression estimate. Therefore confidence intervals for expectiles based on an asymptotic normal distribution are introduced. Their properties are investigated by a simulation study and compared to a boostrap-based gold standard method. Finally the introduced confidence intervals help to evaluate a geoadditive expectile regression model on childhood malnutrition data from India.

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Section: Expectilesmentioning

confidence: 99%

On confidence intervals for semiparametric expectile regression

et al. 2011

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“…Spatial or other bivariate effects can be incorporated by setting up a bivariate tensor product extension of P -splines for two continuous variables (Kneib, Hothorn, and Tutz 2009). Another way to include spatial effects is the adaptation of Markov random fields for modeling a neighborhood structure (Sobotka and Kneib 2012) or radial basis functions (Hofner 2011). Constrained effects such as monotonic or cyclic effects can be specified as well (Hofner, Müller, and Hothorn 2011;Hofner, Kneib, and Hothorn 2016a).…”

Section: Base-learnersmentioning

confidence: 99%

gamboostLSS: An R Package for Model Building and Variable Selection in the GAMLSS Framework

Hofner¹,

Mayr²,

Schmid³

2016

J. Stat. Soft.

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Generalized additive models for location, scale and shape are a flexible class of regression models that allow to model multiple parameters of a distribution function, such as the mean and the standard deviation, simultaneously. With the R package gamboostLSS, we provide a boosting method to fit these models. Variable selection and model choice are naturally available within this regularized regression framework. To introduce and illustrate the R package gamboostLSS and its infrastructure, we use a data set on stunted growth in India. In addition to the specification and application of the model itself, we present a variety of convenience functions, including methods for tuning parameter selection, prediction and visualization of results. The package gamboostLSS is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=gamboostLSS.

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“…As an example we analyze growth data of Dutch children (Van Buuren and Fredriks 2001) from the R package expectreg (Sobotka et al 2012). The relation between age and weight-especially for babies-is often illustrated by means of percentiles, e.g.…”

Section: Examplesmentioning

confidence: 99%

Simultaneous estimation of quantile curves using quantile sheets

Schnabel

Eilers

2012

AStA Adv Stat Anal

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The results of quantile smoothing often show crossing curves, in particular, for small data sets. We define a surface, called a quantile sheet, on the domain of the independent variable and the probability. Any desired quantile curve is obtained by evaluating the sheet for a fixed probability. This sheet is modeled by P-splines in form of tensor products of B-splines with difference penalties on the array of coefficients. The amount of smoothing is optimized by cross-validation. An application for reference growth curves for children is presented.

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Geoadditive expectile regression

Cited by 118 publications

References 14 publications

On confidence intervals for semiparametric expectile regression

On confidence intervals for semiparametric expectile regression

gamboostLSS: An R Package for Model Building and Variable Selection in the GAMLSS Framework

Simultaneous estimation of quantile curves using quantile sheets

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