Ridge regression splines with knot selection via ℓ0 penalty†
Eun-Ji Lee1 · Jae-Hwan Jhong2
1Department of Statistics, Chungbuk National University
2Department of Information Statistics, Chungbuk National University
2Department of Information Statistics, Chungbuk National University
Correspondence to: † This research was supported by Chungbuk National University Korea National University Development Project (2023).
1 PhD student, Department of Statistics, Chung Buk National University, Cheongju 28644, Korea
2 Corresponding author: Department of Information Statistics, Chung Buk National University, Cheongju 28644, Korea. E-mail: jjh25@chungbuk.ac.kr
1 PhD student, Department of Statistics, Chung Buk National University, Cheongju 28644, Korea
2 Corresponding author: Department of Information Statistics, Chung Buk National University, Cheongju 28644, Korea. E-mail: jjh25@chungbuk.ac.kr
Received July 29, 2024; Revised September 23, 2024; Accepted September 24, 2024.
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
- The Ridge regression model that considers the ℓ2-norm penalty is a model that can alleviate multicollinearity problems by slightly reducing all coefficients in high-dimensional data. When the ℓ0-norm penalty is considered in a linear regression model, variable selection is explicitly performed to build a model using the fewest variables, and a sparse model is created to facilitate interpretation and prevent overfitting. From a nonparametric regression perspective, the knot selection problem can be solved using a norm penalty with a regression model using a combined truncated power spline. We propose estimator based ℓ2-norm and ℓ0-norm penalties. We estimate the coefficients of the regression model with a coordinate descent algorithm. We evaluate the performance of ℓ2-norm and ℓ0-norm penalty-based estimation through three simulations and we present numerical studies through real data analysis.
- Keywords : Best subset selection, coordinate descent algorithm, knot selection, ridge penalty, truncated power splines
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