An analysis of life expectancy and economic production using expectile frontier zones

Schnabel, Sabine; Eilers, Paul H.C.

doi:10.4054/demres.2009.21.5

Cited by 34 publications

(18 citation statements)

References 42 publications

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“…Taylor (2008) applied generalized quantiles to calculate Value at Risk (VaR) and expected shortfall (ES) for financial risk management. Generalized quantiles were used by Schnabel and Eilers (2009a) to study the relationship between GDP and population, and by Härdle and Song (2010) to study the correlation of the wage and the level of education.…”

Section: Introductionmentioning

confidence: 99%

Functional Data Analysis of Generalized Quantile Regressions

et al. 2013

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Generalized quantile regressions, including the conditional quantiles and expectiles as special cases, are useful alternatives to the conditional means for characterizing a conditional distribution, especially when the interest lies in the tails. We develop a functional data analysis approach to jointly estimate a family of generalized quantile regressions. Our approach assumes that the generalized quantile regressions share some common features that can be summarized by a small number of principal component functions. The principal component functions are modeled as splines and are estimated by minimizing a penalized asymmetric loss measure. An iterative least asymmetrically weighted squares algorithm is developed for computation. While separate estimation of individual generalized quantile regressions usually suffers from large variability due to lack of sufficient data, by borrowing strength across data sets, our joint estimation approach significantly improves the estimation efficiency, which is demonstrated in a simulation study. The proposed method is applied to data from 150 weather stations in China to obtain the generalized quantile curves of the volatility of the temperature at these stations. These curves are needed to adjust temperature risk factors so that gaussianity is achieved. The normal distribution of temperature variations is vital for pricing weather derivatives with tools from mathematical finance.

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Section: Introductionmentioning

confidence: 99%

Functional Data Analysis of Generalized Quantile Regressions

et al. 2013

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“…In our previous work on expectile smoothing (e.g. in Schnabel & Eilers, ), we also encountered minor problems with crossing expectile curves. However, in our experience, intersecting curves are a less frequent problem in expectiles than with the currently available quantile estimation techniques.…”

Section: Introductionmentioning

confidence: 98%

A location‐scale model for non‐crossing expectile curves

Schnabel

Eilers

2013

Stat

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In quantile smoothing, crossing of the estimated curves is a common nuisance, in particular with small data sets and dense sets of quantiles. Similar problems arise in expectile smoothing. We propose a novel method to avoid crossings. It is based on a location-scale model for expectiles and estimates all expectile curves simultaneously in a bundle using iterative least asymmetrically weighted squares. In addition, we show how to estimate a density non-parametrically from a set of expectiles. The model is applied to two data sets.

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“…Kuan et al (2009) considered the conditional autoregressive expectile (CARE) model to calculate the VaR, and expectiles are used to calculate the expected shortfall in Taylor (2008). Schnabel and Eilers (2009a) modelled the relationship between gross domestic product per capita (GDP) and average life expectancy using expectile curves. There are several methods to calculate the expectiles.…”

Section: Introductionmentioning

confidence: 99%

A Confidence Corridor for Expectile Functions

Duran

Guo²,

Härdle

2011

SSRN Journal

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Let (X 1 , Y 1 ), . . ., (X n , Y n ) be i.i.d. rvs and denote v(x) as the unknown τ -expectile regression curve of Y conditional on X. We introduce the expectilesmoother v n (x) as a localized nonlinear estimator of v(x), and prove the strong uniform consistency rate of v n (x) under general conditions. The stochastic fluctuation of the process {v n (x) − v(x)} is also studies in our paper. Moreover, using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation sup 0 x 1 |v n (x)−v(x)|. This paper considers fitting a simultaneous confidence corridor (SCC) around the estimated expectile function of the conditional distribution of Y given x based on the observational data generated according to a nonparametric regression model. Furthermore, we apply it into the temperature analysis. We construct the simultaneous confidence corridors around the expectiles of the residuals from the temperature models to investigate the temperature risk drivers. We find the risk drivers in Berlin and Taipei are different.

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An analysis of life expectancy and economic production using expectile frontier zones

Cited by 34 publications

References 42 publications

Functional Data Analysis of Generalized Quantile Regressions

Functional Data Analysis of Generalized Quantile Regressions

A location‐scale model for non‐crossing expectile curves

A Confidence Corridor for Expectile Functions

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