• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.189-199
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• 2020

This paper studies a Bayesian ordered multiple linear regression model with skew normal error. It is reasonable that the kind of inherent information available in an applied regression requires some constraints on the coefficients to be estimated. In addition, the assumption of normality of the errors is sometimes not appropriate in the real data. Therefore, to explain such situations more flexibly, we use the skew-normal distribution given by Sahu et al. (The Canadian Journal of Statistics, 31, 129-150, 2003) for error-terms including normal distribution. For Bayesian methodology, the Markov chain Monte Carlo method is employed to resolve complicated integration problems. Also, under the improper priors, the propriety of the associated posterior density is shown. Our Bayesian proposed model is applied to NZAPB's apple data. For model comparison between the skew normal error model and the normal error model, we use the Bayes factor and deviance information criterion given by Spiegelhalter et al. (Journal of the Royal Statistical Society Series B (Statistical Methodology), 64, 583-639, 2002). We also consider the problem of detecting an influential point concerning skewness using Bayes factors. Finally, concluding remarks are discussed.

• The Korean Journal of Applied Statistics
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• v.31 no.3
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• pp.367-382
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• 2018

Prediction models for a corporate bond rating in existing studies have been developed using various models such as linear regression, ordered logit, and random forest. Financial characteristics help build prediction models that are expected to be contained in the assigning model of the bond rating agencies. However, the ranges of bond ratings in existing studies vary from 5 to 20 and the prediction models were developed with samples in which the target companies and the observation periods are different. Thus, a simple comparison of the prediction accuracies in each study cannot determine the best prediction model. In order to conduct a fair comparison, this study has collected corporate bond ratings and financial characteristics from 2013 to 2017 and applied prediction models to them. In addition, we applied the elastic-net penalty for the linear regression, the ordered logit, and the ordered probit. Our comparison shows that data-driven variable selection using the elastic-net improves prediction accuracy in each corresponding model, and that the random forest is the most appropriate model in terms of prediction accuracy, which obtains 69.6% accuracy of the exact rating prediction on average from the 5-fold cross validation.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.565-579
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• 1997

A robust test is proposed for the problem of testing the parallelism of several regression lines against ordered alternatives. The proposed test statistic is based on a linear combination of one-step pairwise GM-estimators. We compare the performance of the proposed test with that of the other tests through a Monte Carlo simulation. The results of the simulation study show that the proposed test has stable levels, good empirical powers in various circumstances, and particularly higher empirical powers under the presence of extreme outliers or leverage points.

• Journal of Korean Society for Quality Management
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• v.17 no.2
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• pp.70-80
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• 1989

A nonparametric test for testing the parallelism of regression lines against ordered alternatives is proposed. The proposed test statistic is based on a linear combination of robust slope estimators. It is a modified version of the Adichie's test statistics based on scores. A snail-sample Monte Carlo study shows that the proposed test is compatible with the Adichie's test.

• Journal of Korean Society for Quality Management
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• v.21 no.2
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• pp.162-169
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• 1993

For the problem of testing the parallelism of several regression lines against ordered alternatives, two test statistics and proposed and examined. The proposed statistics are linear combinations of robust estimators of slope parameters, which are modifications of the Adichie (1976) test based on scores. The asymptotic null variances of the proposed states tics are estimated by the kernel density estimation methods. The proposed tests are compared with the Adichie's test in terms of asymptotic relative efficiency and small-sample powers.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.489-497
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• 1996

Lower bounds for the full level probabilities are derived under order restrictions in weights. Discussions are made on typical isotonic cones such as linear order, simple tree order, and unimodal order cones. We also discuss applications of these results for constructing conditional likelihood ratio tests for ordered hypotheses in a contingency table. A real data set on torus mandibularis will be analyzed for illustrating the testing procedure.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.471-485
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• 2016

Least squares (LS) regression is a classic method for regression that is optimal under assumptions of regression and usual observations. However, the presence of unusual data in the LS method leads to seriously distorted estimates. Therefore, various robust estimation methods are proposed to circumvent the limitations of traditional LS regression. Among these, there are M-estimators based on maximum likelihood estimation (MLE), L-estimators based on linear combinations of order statistics and R-estimators based on a linear combinations of the ordered residuals. In this paper, robust regression estimators with high breakdown point and/or with high efficiency are compared under several simulated situations. The paper analyses and compares distributions of estimates as well as relative efficiencies calculated from mean squared errors (MSE) in the simulation study. We conclude that MM-estimators or GR-estimators are a good choice for the real data application.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.179-182
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• 2003

This study describes a new graphical method for assessing and characterizing effect modification by a matching covariate in matched case-control studies. This method to understand effect modification is based on a semiparametric model using a varying coefficient model. The method allows for nonparametric relationships between effect modification and other covariates, or can be useful in suggesting parametric models. This method can be applied to examining effect modification by any ordered categorical or continuous covariates for which cases have been matched with controls. The method applies to effect modification when causality might be reasonably assumed. An example from veterinary medicine is used to demonstrate our approach. The simulation results show that this method, when based on linear, quadratic and nonparametric effect modification, can be more powerful than both a parametric multiplicative model fit and a fully nonparametric generalized additive model fit.

• Water for future
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• v.20 no.2
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• pp.117-126
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• 1987

A Synthetic unit hydrograph method was suggested for the representation of a direct runoff hydrograph with empirical geomorphologic laws and geomorphologic parameters by applying geomorphologic instantaneous unit hydrograph theory and Rossois results of application of GIUH theory to the Nash Model which is a linear reservoir model. The shape parameter m and scale parameter k can be derived by the Horton's empirical geomorphologic laws $R_A,R_B,R_L$ when ordered according to Strahler's ordering Scheme, main stream length and using the maximum velocity for the dynamic characteristics of a river basin, The derived response function was tested on some observed flood datas and showed promising. For the determination of the shape parameter m, eq. (16) was showed applying and m showed a good regression with the size of basin area.

• Journal of Korea Water Resources Association
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• v.49 no.11
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• pp.941-949
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• 2016

The flow characteristics of the broad-crested side weir considering the levee's side slope of main channel ($ES_{ch}$) was investigated through hydraulic experiment in order to estimate the discharge coefficient equation. For applicability to actual river, levee's side slope of main channel 1:0.5, 1:1 and 1:2 were selected. Experimental results show that the new estimated equation for the discharge coefficient including $ES_{ch}$ is reasonable and effective in actual applications by comparing estimated and measured discharge over side weirs. Through a multiple linear regression analysis the importance of variabes were ordered as $ES_{ch}$ > $h/y_u$ > $L/y_u$ > $Fr_u$. Especially the discharge coefficient equation without $Fr_u$ was suggested, and the high applicability was reviewed by comparing the measured and calculated overflow of broad-chested side weir.