• 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.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.749-756
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• 2012

An approach widely used for small area estimation is based on linear mixed models. However, when the functional form of the relationship between the response and the input variables is not linear, it may lead to biased estimators of the small area parameters. In this paper we propose M-quantile kernel regression for small area mean estimation allowing nonlinearities in the relationship between the response and the input variables. Numerical studies are presented that show the sample properties of the proposed estimation method.

• 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.

• Journal of the Korean Geophysical Society
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• v.5 no.2
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• pp.131-142
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• 2002

Geomagnetic transfer function is generally estimated by choosing transfer to minimize the square sum of differences between observed values. If the error structure sccords to the Gaussian distribution, standard least square(LS) can be the estimation. However, for non-Gaussian error distribution, the LS estimation can be severely biased and distorted. In this paper, the Gaussian error assumption was tested by Q-Q(Quantile-Quantile) plot which provided information of real error structure. Therefore, robust estimation such as regression M-estimate that does not allow a few bad points to dominate the estimate was applied for error structure with non-Gaussian distribution. The results indicate that the performance of robust estimation is similar to the one of LS estimation for Gaussian error distribution, whereas the robust estimation yields more reliable and smooth transfer function estimates than standard LS for non-Gaussian error distribution.

• Communications for Statistical Applications and Methods
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• v.30 no.6
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• pp.531-550
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• 2023

The estimation of extreme quantiles is one of the main objectives of statistics of extremes (which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regression model. The proposed estimator was compared with two estimators of extreme quantiles in the literature in a simulation study. The results show that the proposed estimator is stable to the choice of the number of top order statistics and show lesser bias and mean square error compared to the existing extreme quantile estimators. Practical application of the proposed estimator is illustrated with data from the pedochemical and insurance industries.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.377-383
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• 2016

The set of priors in the representation of coherent risk measure is expressed in terms of quantile function and increasing concave function. We show that the set of prior, $\mathcal{Q}_c$ in (1.2) is equal to the set of $\mathcal{Q}_m$ in (1.6), as maximal representing set $\mathcal{Q}_{max}$ defined in (1.7).

• International Journal of Reliability and Applications
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• v.9 no.1
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• pp.53-70
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• 2008

In this paper, we discuss the plethora of uses for the software package R, and focus specifically on its helpful applications in reliability data analyses. Examples are presented; including the R coding protocol, R code, and plots for various statistical as well as reliability analyses. We explore Kaplan-Meier estimates and maximum likelihood estimation for distributions including the Weibull. Finally, we discuss future applications of R, and usages of quantile regression in reliability.

• Journal of Korea Water Resources Association
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• v.46 no.8
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• pp.833-842
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• 2013

The quantile mapping is utilized to reproduce reliable GCM(Global Climate Model) data by correct systematic biases included in the original data set. This scheme, in general, projects the Cumulative Distribution Function (CDF) of the underlying data set into the target CDF assuming that parameters of target distribution function is stationary. Therefore, the application of stationary quantile mapping for nonstationary long-term time series data of future precipitation scenario computed by GCM can show biased projection. In this research the Nonstationary Quantile Mapping (NSQM) scheme was suggested for bias correction of nonstationary long-term time series data. The proposed scheme uses the statistical parameters with nonstationary long-term trends. The Gamma distribution was assumed for the object and target probability distribution. As the climate change scenario, the 20C3M(baseline scenario) and SRES A2 scenario (projection scenario) of CGCM3.1/T63 model from CCCma (Canadian Centre for Climate modeling and analysis) were utilized. The precipitation data were collected from 10 rain gauge stations in the Han-river basin. In order to consider seasonal characteristics, the study was performed separately for the flood (June~October) and nonflood (November~May) seasons. The periods for baseline and projection scenario were set as 1973~2000 and 2011~2100, respectively. This study evaluated the performance of NSQM by experimenting various ways of setting parameters of target distribution. The projection scenarios were shown for 3 different periods of FF scenario (Foreseeable Future Scenario, 2011~2040 yr), MF scenario (Mid-term Future Scenario, 2041~2070 yr), LF scenario (Long-term Future Scenario, 2071~2100 yr). The trend test for the annual precipitation projection using NSQM shows 330.1 mm (25.2%), 564.5 mm (43.1%), and 634.3 mm (48.5%) increase for FF, MF, and LF scenarios, respectively. The application of stationary scheme shows overestimated projection for FF scenario and underestimated projection for LF scenario. This problem could be improved by applying nonstationary quantile mapping.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.325-335
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• 2002

In this paper we introduce some adaptive M-estimators using selector statistics to estimate the center of symmetric and continuous underlying distributions. This selector statistics is based on the idea of Hogg(1983) and Hogg et. al. (1988) who used averages of some order statistics to discriminate underlying distributions. In this paper, we use the functions of sample quantiles as selector statistics and determine the suitable quantile points based on maximizing the distance index to discriminate distributions under consideration. In Monte Carlo study, this robust estimation method works pretty good in wide range of underlying distributions.

• Journal of Korean Society on Water Environment
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• v.31 no.3
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• pp.241-252
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• 2015

Runoff behaviors by five bias correction methods were analyzed, which were Change Factor methods using past observed and estimated data by the estimation scenario with average annual calibration factor (CF_Y) or with average monthly calibration factor (CF_M), Quantile Mapping methods using past observed and estimated data considering cumulative distribution function for entire estimated data period (QM_E) or for dry and rainy season (QM_P), and Integrated method of CF_M+QM_E(CQ). The peak flow by CF_M and QM_P were twice as large as the measured peak flow, it was concluded that QM_P method has large uncertainty in monthly runoff estimation since the maximum precipitation by QM_P provided much difference to the other methods. The CQ method provided the precipitation amount, distribution, and frequency of the smallest differences to the observed data, compared to the other four methods. And the CQ method provided the rainfall-runoff behavior corresponding to the carbon dioxide emission scenario of SRES A1B. Climate change scenario with bias correction still contained uncertainty in accurate climate data generation. Therefore it is required to consider the trend of observed precipitation and the characteristics of bias correction methods so that the generated precipitation can be used properly in water resource management plan establishment.