Browse > Article
http://dx.doi.org/10.5351/KJAS.2021.34.6.937

Variable selection in partial linear regression using the least angle regression  

Seo, Han Son (Department of Applied Statistics, Konkuk University)
Yoon, Min (Department of Applied Mathematics, Pukyong National University)
Lee, Hakbae (Department of Applied Statistics, Yonsei University)
Publication Information
The Korean Journal of Applied Statistics / v.34, no.6, 2021 , pp. 937-944 More about this Journal
Abstract
The problem of selecting variables is addressed in partial linear regression. Model selection for partial linear models is not easy since it involves nonparametric estimation such as smoothing parameter selection and estimation for linear explanatory variables. In this work, several approaches for variable selection are proposed using a fast forward selection algorithm, least angle regression (LARS). The proposed procedures use t-test, all possible regressions comparisons or stepwise selection process with variables selected by LARS. An example based on real data and a simulation study on the performance of the suggested procedures are presented.
Keywords
least angle regression; partial linear models; sequential selection; variable selection; LARS;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Akaike H (1973). Information theory and an extension of the maximum likelihood principle. In Proceedings of the 2nd International Symposium on Information Theory, 267-281, Budapest.
2 Akaike H (1974). A new look a the statistical model identification, IEEE Transactions on Automatic Control, 19, 716-723.   DOI
3 Aneiros G, Ferraty F, and Vieu P (2015). Variable selection in partial linear regression with functional covariate, Statistics, 49, 1322-1347.   DOI
4 Chen, H. and Chen, K.(1991). Selection of the splined variables and convergence rates in a partial spline model, The Canadian Journal of Statistics, 19, 323-339.   DOI
5 Fan J and Peng H (2004). Nonconcave penalized likelihood with a diverging number of parameters, Annals of Statistics, 32, 928-961.   DOI
6 Ni X, Zhang H, and Zhang D (2009). Automatic model selection for partially linear models, Journal of Multivariate Analysis, 100, 2100-2111.   DOI
7 Xie H and Huang J (2009). SCAD-penalized regression in high-dimensional partially linear model, Annals of Statistics, 37, 673-696.   DOI
8 Efron B, Hastie T, Johnstone I, and Tibshirani R (2004). Least angle regression, The Annals of Statistics, 32, 407-499.   DOI
9 Bunea F (2004). Consistent covariate selection and post model selection inference in semiparametric regression, Annals of Statistics, 32, 898-927.   DOI
10 Bunea F and Wegkamp M (2004). Two-stage model selection procedures in partially linear regression, The Canadian Journal of Statistics, 32, 105-118.   DOI
11 Fan J and Li R (2004). New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis, Journal of American Statistical Association, 99, 710-723.   DOI
12 Hardle W, Liang H, and Gao J (2000). Partially Linear Models, Physica-Verlag, Heidelberg.
13 McCann L and Welsch R (2007). Robust variable selection using least angle regression and elemental set sampling, Computational Statistics and Data Analysis, 52, 249-257.   DOI
14 Schwarz G (1978). Some comments on Cp, Technometrics, 15, 662-676.