• The Korean Journal of Applied Statistics
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• v.26 no.6
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• pp.915-922
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• 2013

Quantile regression can estimate multiple conditional quantile functions of the response, and as a result, it provide comprehensive information of the relationship between the response and the predictors. However, when estimating several conditional quantile functions separately, two or more estimated quantile functions may cross or overlap and consequently violate the basic properties of quantiles. In this paper, we propose a new stepwise method to estimate multiple non-crossing quantile functions using constraints on the kernel coefficients. A simulation study are presented to demonstrate satisfactory performance of the proposed method.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.807-818
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• 2005

In this paper we propose an estimation method for regression quantiles with left-truncated and right-censored data. The estimation procedure is based on the weight determined by the Kaplan-Meier estimate of the distribution of the response. We show how the proposed regression quantile estimators perform through analyses of Stanford heart transplant data and AIDS incubation data. We also investigate the effect of censoring on regression quantiles through simulation study.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.457-465
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• 2011

Sample entropy (Vasicek, 1976) has poor performance, and several nonparametric entropy estimators have been proposed as alternatives. In this paper, we consider a piecewise uniform density function based on quantiles, which enables us to evaluate entropy in each interval, and study the poor performance of the sample entropy in terms of the poor estimation of lower and upper quantiles. Then we propose some improved entropy estimators by simply modifying the quantile estimators, and compare their performances with some existing estimators.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.1091-1102
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• 2003

The Weibull variate is commonly used as a lifetime distribution in reliability applications. Estimation of parameters is revisited in the two-parameter Weibull distribution. The method of product spacings, the method of quantile estimates and the method of least squares are applied to this distribution. A comparative study between a simple minded estimate, the maximum likelihood estimate, the product spacings estimate, the quantile estimate, the least squares estimate, and the adjusted least squares estimate is presented.

• The Korean Journal of Applied Statistics
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• v.21 no.4
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• pp.631-638
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• 2008

Accelerated Lifetime Test is a method of estimation of lifetime quality characteristics under operation condition with the accelerated lifetime data obtained under accelerated stress. In this paper we propose estimation method with accelerated lifetime data using quantile regression. We apply the method to real data with Arrhenius and Inverse power model.

• 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.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.753-764
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• 2008

The $L_1$ regularized estimator in quantile problems conduct parameter estimation and model selection simultaneously and have been shown to enjoy nice performance. However, $L_1$ regularized estimator has a drawback: when there are several highly correlated variables, it tends to pick only a few of them. To make up for it, the proposed method adopts doubly regularized framework with the mixture of $L_1$ and $L_2$ norms. As a result, the proposed method can select significant variables and encourage the highly correlated variables to be selected together. One of the most appealing features of the new algorithm is to construct the entire solution path of doubly regularized quantile estimator. From simulations and real data analysis, we investigate its performance.

• Proceedings of the Korean Association for Survey Research Conference
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• 2006.12a
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• pp.67-83
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• 2006

In successive sampling on two occasions the problem of estimating a finite population quantile has been considered. The theory developed aims at providing the optimum estimates by combining (i) three double sampling estimators viz. ratio-type, product-type and regression-type, from the matched portion of the sample and (ii) a simple quantile based on a random sample from the unmatched portion of the sample on the second occasion. The approximate variance formulae of the suggested estimators have been obtained. Optimal matching fraction is discussed. A simulation study is carried out in order to compare the three estimators and direct estimator. It is found that the performance of the regression-type estimator is the best among all the estimators discussed here.

• Journal of the Korean Statistical Society
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• v.36 no.4
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• pp.543-556
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• 2007

In successive sampling on two occasions the problem of estimating a finite population quantile has been considered. The theory developed aims at providing the optimum estimates by combining (i) three double sampling estimators viz. ratio-type, product-type and regression-type, from the matched portion of the sample and (ii) a simple quantile based on a random sample from the unmatched portion of the sample on the second occasion. The approximate variance formulae of the suggested estimators have been obtained. Optimal matching fraction is discussed. A simulation study is carried out in order to compare the three estimators and direct estimator. It is found that the performance of the regression-type estimator is the best among all the estimators discussed here.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.677-684
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• 2014

Support vector quantile regression (SVQR) is capable of providing more complete description of the linear and nonlinear relationships among random variables. To improve the estimation performance of SVQR we propose to use SVQR ensemble with bagging (bootstrap aggregating), in which SVQRs are trained independently using the training data sets sampled randomly via a bootstrap method. Then, they are aggregated to obtain the estimator of the quantile regression function using the penalized objective function composed of check functions. Experimental results are then presented, which illustrate the performance of SVQR ensemble with bagging.