• The Korean Journal of Applied Statistics
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• v.31 no.3
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• pp.343-352
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• 2018

We can use quantile regression and expectile regression analysis to estimate trends in extreme regions as well as the average trends of response variables in given explanatory variables. In this paper, we compare the performance between the parametric and nonparametric methods for expectile regression. We introduce each estimation method and analyze through various simulations and the application to real data. The nonparametric model showed better results if the model is complex and difficult to deduce the relationship between variables. The use of nonparametric methods can be recommended in terms of the difficulty of assuming a parametric model in expectile regression.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.931-939
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• 2014

In this paper we propose the iteratively reweighted least squares procedure to solve the quadratic programming problem of support vector expectile regression with an asymmetrically weighted squares loss function. The proposed procedure enables us to select the appropriate hyperparameters easily by using the generalized cross validation function. Through numerical studies on the artificial and the real data sets we show the effectiveness of the proposed method on the estimation performances.

• Journal of the Korean Data and Information Science Society
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• v.24 no.3
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• pp.625-636
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• 2013

In this paper we study four kernel machines for estimating expected shortfall, which are constructed through combinations of support vector quantile regression (SVQR), restricted SVQR (RSVQR), least squares support vector machine (LS-SVM) and support vector expectile regression (SVER). These kernel machines have obvious advantages such that they achieve nonlinear model but they do not require the explicit form of nonlinear mapping function. Moreover they need no assumption about the underlying probability distribution of errors. Through numerical studies on two artificial an two real data sets we show their effectiveness on the estimation performance at various confidence levels.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.171-180
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• 2016

Basel committee suggests using Value-at-Risk (VaR) and expected shortfall (ES) as a measurement for market risk. Various estimation methods of VaR and ES have been studied in the literature. This paper compares semi-parametric methods, such as conditional autoregressive value at risk (CAViaR) and conditional autoregressive expectile (CARE) methods, and a Gaussian quasi-maximum likelihood estimator (QMLE)-based method through back-testing methods. We use unconditional coverage (UC) and conditional coverage (CC) tests for VaR, and a bootstrap test for ES to check the adequacy. A real data analysis is conducted for S&P 500 index and Hyundai Motor Co. stock price index data sets.

• Journal of the Korean Data and Information Science Society
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• v.22 no.5
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• pp.999-1005
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• 2011

This paper proposes a weighted least squares support vector machine for asymmetric least squares regression. This method achieves nonlinear prediction power, while making no assumption on the underlying probability distributions. The cross validation function is introduced to choose optimal hyperparameters in the procedure. Experimental results are then presented which indicate the performance of the proposed model.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.973-981
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• 2010

Quantile regression investigates the quantiles of the conditional distribution of a response variable given a set of covariates. M-quantile regression extends this idea by a "quantile-like" generalization of regression based on influence functions. In this paper we propose a new method of estimating M-quantile regression functions, which uses kernel machine technique. Simulation studies are presented that show the finite sample properties of the proposed M-quantile regression.