@article{wang_shin_wu_2018, title={Principal quantile regression for sufficient dimension reduction with heteroscedasticity}, volume={12}, ISSN={["1935-7524"]}, DOI={10.1214/18-EJS1432}, abstractNote={: Suﬃcient dimension reduction (SDR) is a successful tool for re- ducing data dimensionality without stringent model assumptions. In practice, data often display heteroscedasticity which is of scientiﬁc importance in general but frequently overlooked since a primal goal of most existing statistical methods is to identify conditional mean relationship among variables. In this article, we propose a new SDR method called principal quantile regression (PQR) that eﬃciently tackles heteroscedasticity. PQR can naturally be extended to a nonlinear version via kernel trick. Asymptotic properties are established and an eﬃcient solution path-based algo- rithm is provided. Numerical examples based on both simulated and real data demonstrate the PQR’s advantageous performance over existing SDR methods. PQR still performs very competitively even for the case without heteroscedasticity.}, number={2}, journal={ELECTRONIC JOURNAL OF STATISTICS}, author={Wang, Chong and Shin, Seung Jun and Wu, Yichao}, year={2018}, pages={2114–2140} }
@article{shin_wu_zhang_2014, title={Two-dimensional solution surface for weighted support vector machines}, volume={23}, DOI={10.1080/10618600.2012.761139}, abstractNote={The support vector machine (SVM) is a popular learning method for binary classification. Standard SVMs treat all the data points equally, but in some practical problems it is more natural to assign different weights to observations from different classes. This leads to a broader class of learning, the so-called weighted SVMs (WSVMs), and one of their important applications is to estimate class probabilities besides learning the classification boundary. There are two parameters associated with the WSVM optimization problem: one is the regularization parameter and the other is the weight parameter. In this article, we first establish that the WSVM solutions are jointly piecewise-linear with respect to both the regularization and weight parameter. We then develop a state-of-the-art algorithm that can compute the entire trajectory of the WSVM solutions for every pair of the regularization parameter and the weight parameter at a feasible computational cost. The derived two-dimensional solution surface provides theoretical insight on the behavior of the WSVM solutions. Numerically, the algorithm can greatly facilitate the implementation of the WSVM and automate the selection process of the optimal regularization parameter. We illustrate the new algorithm on various examples. This article has online supplementary materials.}, number={2}, journal={Journal of Computational and Graphical Statistics}, author={Shin, S. J. and Wu, Y. C. and Zhang, H. H.}, year={2014}, pages={383–402} }
@article{jhun_shin_2009, title={Bootstrapping Spatial Median for Location Problems}, volume={38}, ISSN={["0361-0918"]}, DOI={10.1080/03610910903249528}, abstractNote={In multivariate location problems, the sample mean is most widely used, having various advantages. It is, however, very sensitive to outlying observations and inefficient for data from heavy tailed distributions. In this situation, the spatial median is more robust than the sample mean and could be a reasonable alternative. We reviewed several spatial median based testing methods for multivariate location and compared their significance level and power through Monte Carlo simulations. The results show that bootstrap method is efficient for the estimation of the covariance matrix of the sample spatial median. We also proposed bootstrap simultaneous confidence intervals based on the spatial median for multiple comparisons in the multi-sample case.}, number={10}, journal={COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION}, author={Jhun, Myoungshic and Shin, Seungjun}, year={2009}, pages={2123–2133} }