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Mixed degree regression function estimation using weighted lasso penalty
Journal of the Korean Data & Information Science Society 2022;33:517-31
Published online May 31, 2022;  https://doi.org/10.7465/jkdi.2022.33.3.517
© 2022 Korean Data and Information Science Society.

Eun-Ji Lee1 · Jae-Hwan Jhong2

12Department of Information Statistics, Chungbuk National University
Correspondence to: This work was supported by the research grant of the Chungbuk National University in 2020.
1 Graduate student of master degree, Department of Information Statistics, Chungbuk National University, Cheongju 28644, Chungbuk, Korea.
2 Assistant professor, Department of Information Statistics, Chungbuk National University, Cheongju 28644, Chungbuk, Korea. E-mail: jjh25@cbnu.ac.kr
Received March 10, 2022; Revised April 13, 2022; Accepted April 22, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider a nonparametric function estimation method with mixed degree using weighted lasso penalty. The l1 norm penalty controls linear and cubic trends depending on the value of the parameter. In the proposed estimator, we introduce one computational algorithm for constrained convex optimization problems corresponding to the Lagrangian dual problem based on quadratic programming. Subsequently, using simulations and two real data analyses, numerical studies are conducted to verify the performance of the estimator of the proposed method by identifying the relationship between the data.
Keywords : Knot selection, quadratic programming, splines, weighted lasso.