• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.643-656
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• 2016

High dimensional data are frequently encountered in various fields where the number of variables is greater than the number of samples. It is usually necessary to select variables to estimate regression coefficients and avoid overfitting in high dimensional data. A penalized regression model simultaneously obtains variable selection and estimation of coefficients which makes them frequently used for high dimensional data. However, the penalized regression model also needs to select the optimal model by choosing a tuning parameter based on the model selection criterion. This study deals with the bias effect of LASSO regression for model selection criteria. We numerically describes the bias effect to the model selection criteria and apply the proposed correction to the identification of biomarkers for lung cancer based on gene expression data.

• The Korean Journal of Applied Statistics
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• v.32 no.6
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• pp.909-922
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• 2019

In this paper, we study the adaptive least absolute shrinkage and selection operator (LASSO) for the unstable autoregressive (AR) model. To identify the existence of the unit root, we apply the adaptive LASSO to the augmented Dickey-Fuller regression model, not the original AR model. We illustrate our method with simulations and a real data analysis. Simulation results show that the adaptive LASSO obtained by minimizing the Bayesian information criterion selects the order of the autoregressive model as well as the degree of differencing with high accuracy.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1361-1371
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• 2016

Quantile regression provides a variety of useful statistical information to examine how covariates influence the conditional quantile functions of a response variable. However, traditional quantile regression (which assume a linear model) is not appropriate when the relationship between the response and the covariates is a nonlinear. It is also necessary to conduct variable selection for high dimensional data or strongly correlated covariates. In this paper, we propose a penalized quantile regression tree model. The split rule of the proposed method is based on residual analysis, which has a negligible bias to select a split variable and reasonable computational cost. A simulation study and real data analysis are presented to demonstrate the satisfactory performance and usefulness of the proposed method.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.217-227
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• 2022

Quantile regression is widely used in many fields based on the advantage of providing an efficient tool for examining complex information latent in variables. However, modern large-scale and high-dimensional data makes it very difficult to estimate the quantile regression model due to limitations in terms of computation time and storage space. Divide-and-conquer is a technique that divide the entire data into several sub-datasets that are easy to calculate and then reconstruct the estimates of the entire data using only the summary statistics in each sub-datasets. In this paper, we studied on a variable selection method using Bayes information criteria by applying the divide-and-conquer technique to the penalized quantile regression. When the number of sub-datasets is properly selected, the proposed method is efficient in terms of computational speed, providing consistent results in terms of variable selection as long as classical quantile regression estimates calculated with the entire data. The advantages of the proposed method were confirmed through simulation data and real data analysis.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.499-510
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• 2016

It is very important to select relevant variables in regression models for survival analysis. In this paper, we introduce a penalized variable-selection procedure in multi-level frailty models based on the "frailtyHL" R package (Ha et al., 2012). Here, the estimation procedure of models is based on the penalized hierarchical likelihood, and three penalty functions (LASSO, SCAD and HL) are considered. The proposed methods are illustrated with multi-country/multi-center bladder cancer survival data from the EORTC in Belgium. We compare the results of three variable-selection methods and discuss their advantages and disadvantages. In particular, the results of data analysis showed that the SCAD and HL methods select well important variables than in the LASSO method.

• The Korean Journal of Applied Statistics
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• v.34 no.3
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• pp.411-425
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• 2021

Accelerated failure time (AFT) model represents a linear relationship between the log-survival time and covariates. We are interested in the inference of covariate's effect affecting the variation of survival times in the AFT model. Thus, we need to model the variance as well as the mean of survival times. We call the resulting model mean and variance AFT (MV-AFT) model. In this paper, we propose a variable selection procedure of regression parameters of mean and variance in MV-AFT model using penalized likelihood function. For the variable selection, we study four penalty functions, i.e. least absolute shrinkage and selection operator (LASSO), adaptive lasso (ALASSO), smoothly clipped absolute deviation (SCAD) and hierarchical likelihood (HL). With this procedure we can select important covariates and estimate the regression parameters at the same time. The performance of the proposed method is evaluated using simulation studies. The proposed method is illustrated with a clinical example dataset.

• The Korean Journal of Applied Statistics
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• v.37 no.1
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• pp.1-12
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• 2024

In many real-world data, multiple response variables are often dependent on the same set of explanatory variables. In particular, if several response variables are correlated with each other, simultaneous estimation considering the correlation between response variables might be more effective way than individual analysis by each response variable. In this multivariate regression analysis, least distance estimator (LDE) can estimate the regression coefficients simultaneously to minimize the distance between each training data and the estimates in a multidimensional Euclidean space. It provides a robustness for the outliers as well. In this paper, we examine the least distance estimation method in multivariate linear regression analysis, and furthermore, we present the penalized least distance estimator (PLDE) for efficient variable selection. The LDE technique applied with the adaptive group LASSO penalty term (AGLDE) is proposed in this study which can reflect the correlation between response variables in the model and can efficiently select variables according to the importance of explanatory variables. The validity of the proposed method was confirmed through simulations and real data analysis.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.965-976
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• 2015

Determining relevant variables for a regression model is important in regression analysis. Recently, a variable selection methods using a penalized likelihood with various penalty functions (e.g. LASSO and SCAD) have been widely studied in simple statistical models such as linear models and generalized linear models. The advantage of these methods is that they select important variables and estimate regression coefficients, simultaneously; therefore, they delete insignificant variables by estimating their coefficients as zero. We study how to select proper variables based on penalized hierarchical likelihood (HL) in semi-parametric frailty models that allow three penalty functions, LASSO, SCAD and HL. For the variable selection we develop a new function in the "frailtyHL" R package. Our methods are illustrated with breast cancer survival data from the Medical Center at Chonnam National University in Korea. We compare the results from three variable-selection methods and discuss advantages and disadvantages.

• 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.

• The Korean Journal of Applied Statistics
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• v.35 no.5
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• pp.631-644
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• 2022

This paper considers robust estimation of the sparse vector autoregressive model (sVAR) useful in high-dimensional time series analysis. First, we generalize the result of Xu et al. (2008) that the adaptive lasso indeed has robustness in sVAR as well. However, adaptive lasso method in sVAR performs poorly as the number and sizes of outliers increases. Therefore, we propose new robust estimation methods for sVAR based on least absolute deviation (LAD) and Huber estimation. Our simulation results show that our proposed methods provide more accurate estimation in turn showed better forecasting performance when outliers exist. In addition, we applied our proposed methods to power usage data and confirmed that there are unignorable outliers and robust estimation taking such outliers into account improves forecasting.