• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.673-683
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• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.53-64
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• 2022

High dimensional time series is gaining considerable attention in recent years. The sparse vector heterogeneous autoregressive (VHAR) model proposed by Baek and Park (2020) uses adaptive lasso and debiasing procedure in estimation, and showed superb forecasting performance in realized volatilities. This paper extends the sparse VHAR model by considering non-convex penalties such as SCAD and MCP for possible bias reduction from their penalty design. Finite sample performances of three estimation methods are compared through Monte Carlo simulation. Our study shows first that taking into cross-sectional correlations reduces bias. Second, nonconvex penalties performs better when the sample size is small. On the other hand, the adaptive lasso with debiasing performs well as sample size increases. Also, empirical analysis based on 20 multinational realized volatilities is provided.

• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.209-215
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• 2009

In regression problem, the SCAD estimator proposed by Fan and Li (2001), has many desirable property such as continuity, sparsity and unbiasedness. In this paper, we extend SCAD penalized regression framework to quantile regression and hence, we propose new SCAD penalized quantile estimator on high-dimensions and also present an efficient algorithm. From the simulation and real data set, the proposed estimator performs better than quantile regression estimator with $L_1$ norm.

• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.143-154
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• 2017

A variable selection method based on probabilistic principal component analysis (PCA) using penalized likelihood method is proposed. The proposed method is a two-step variable reduction method. The first step is based on the probabilistic principal component idea to identify principle components. The penalty function is used to identify important variables in each component. We then build a model on the original data space instead of building on the rotated data space through latent variables (principal components) because the proposed method achieves the goal of dimension reduction through identifying important observed variables. Consequently, the proposed method is of more practical use. The proposed estimators perform as the oracle procedure and are root-n consistent with a proper choice of regularization parameters. The proposed method can be successfully applied to high-dimensional PCA problems with a relatively large portion of irrelevant variables included in the data set. It is straightforward to extend our likelihood method in handling problems with missing observations using EM algorithms. Further, it could be effectively applied in cases where some data vectors exhibit one or more missing values at random.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1229-1244
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• 2017

In recent years, as demand for data-based analytical methodologies increases in various fields, optimization methods have been developed to handle them. In particular, various constraints required for problems in statistics and machine learning can be solved by convex optimization. Alternating direction method of multipliers (ADMM) can effectively deal with linear constraints, and it can be effectively used as a parallel optimization algorithm. ADMM is an approximation algorithm that solves complex original problems by dividing and combining the partial problems that are easier to optimize than original problems. It is useful for optimizing non-smooth or composite objective functions. It is widely used in statistical and machine learning because it can systematically construct algorithms based on dual theory and proximal operator. In this paper, we will examine applications of ADMM algorithm in various fields related to statistics, and focus on two major points: (1) splitting strategy of objective function, and (2) role of the proximal operator in explaining the Lagrangian method and its dual problem. In this case, we introduce methodologies that utilize regularization. Simulation results are presented to demonstrate effectiveness of the lasso.