Journal of the Korean Data & http://dx.doi.org/10.7465/jkdi.2017.28.2.461 Information Science Society 한국데이터정보과학회지 2017, 28(2), 461–471 Feature selection in the semivarying coefficient LS-SVR † Changha Hwang 1 · Jooyong Shim 2 1 Department of Applied Statistics, Dankook University 2 Department of Statistics, Inje University Received 22 February 2017, revised 25 March 2017, accepted 27 March 2017 Abstract In this paper we propose a feature selection method identifying important features in the semivarying coefficient model. One important issue in semivarying coefficient model is how to estimate the parametric and nonparametric components. Another issue is how to identify important features in the varying and the constant effects. We propose a feature selection method able to address this issue using generalized cross validation functions of the varying coefficient least squares support vector regression (LS-SVR) and the linear LS-SVR. Numerical studies indicate that the proposed method is quite effective in identifying important features in the varying and the constant effects in the semivarying coefficient model. Keywords: Feature selection, generalized cross validation function, least squares support vector regression, semivarying coefficient model, varying coefficient model. 1. Introduction Hastie and Tibshirani (1993) introduced the varying coefficient model, which is known as powerful and flexible for modeling the dynamic changes of regression coefficients. The varying coefficient model is a useful extension of the classical linear regression model. In the varying coefficient model, the regression coefficients are not set to be constant but are allowed to change with the value of other features called smoothing variables. The varying coefficient model inherits simplicity and easy interpretation of the classical linear regression models and is gaining its popularity in statistics literature in recent years. The introductions, various applications and current research areas of the varying coefficient model can be found in Hoover et al. (1998), and Fan and Zhang (2008). A great deal of attention has been focused on the problem of estimating the varying coefficients. Most of this attention has been paid to using kernel smoothing technique. Fan and Zhang (2008) give an excellent review of the varying coefficient models and discusses three approaches in estimating the coefficient function: kernel smoothing, polynomial splines and smoothing splines. Recently, some more flexible varying coefficient models have been developed and discussed. See, for example, Yang † This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF- 2015R1D1A1A01056582), (NRF-2015S1A3A2046715). 1 Professor, Department of Applied Statistics, Dankook University, Yongin 16890, Korea. 2 Corresponding author: Adjunct Professor, Department of Statistics, Institute of Statistical Information, Inje University, Kimhae 50834, Korea. E-mail: ds1631@hanmail.net