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Abstract Header

Lasso Method with SCAD Penalty for Estimation and Variable Selection in Sequential Models

Yuan, Yiwen
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1720005880628523

Abstract Details

2024, Doctor of Philosophy (Ph.D.), Bowling Green State University, Statistics.
The sequential linear model is widely employed to analyze the dynamic data where the response variable at each time point incorporates the lagged results from the previous time point. With the lagged dependent response variables added to the model longitudinally, the issue of multicollinearity arises. In such situations, the Lasso method proposed by Tibshirani (1996) addresses both parameter estimation and variable selection simultaneously. However, in high-dimensional data and multicollinearity, the Lasso method can introduce bias in coefficient estimation and inconsistency in variable selection. To improve the Lasso method, a number of different penalty terms are proposed. Among the Lasso methods with different penalty terms, selecting an appropriate estimation and variable selection method is challenging work because it requires balancing the trade-off between achieving low bias and maintaining high prediction accuracy. One of the primary inferences in the sequential linear model is to predict the response variable with high accuracy and relatively minimal prediction errors, thereby saving time and expenses. To achieve this goal, we propose the estimation and variable selection method based on the Lasso, named Smoothly Clipped Absolute Deviation Penalty (SCAD) (Fan and Li, 2001), in the sequential linear model. The proposed SCAD method performs effectively in parameter estimation with low bias and variable selection with low predicted errors. In the demonstration of the effectiveness of the proposed method, we conduct the simulations where we compare the SCAD method with other methods including the ordinary least squares (OLS), Lasso, and Adaptive Lasso in both linear regression and sequential linear models. Since time series refers to a sequence of data generated at each time point, where the lagged response variable at each time point is used as a predictor in the subsequent time point model, accounting for errors based on assumptions, we simulate the data in two scenarios: one without time series and the other with time series, considering low-dimension, medium-dimension, and high-dimension cases. The simulation results demonstrate that compared with the other methods, iv the proposed Lasso with SCAD penalty method in the sequential linear model excels in estimation with better accuracy and in variable selection with lower predicted errors. We apply the proposed method to two real data sets. The application results show that the SCAD method demonstrates better performance by effectively balancing variable selection and parameter estimation. Based on the simulation and application results, we can conclude the proposed Lasso with SCAD penalty method in the sequential linear model is more effective in estimation and variable selection, particularly in high-dimensional settings.
Junfeng Shang, Ph. D. (Committee Chair)
John H. Boman, Ph. D. (Other)
Hanfeng Chen, Ph. D. (Committee Member)
John Chen, Ph. D. (Committee Member)
135 p.
Statistics
Sequential Analysis; Biostatistics; Variable Selection; High-dimensional Inference;

Recommended Citations

Citations

  • Yuan, Y. (2024). Lasso Method with SCAD Penalty for Estimation and Variable Selection in Sequential Models [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1720005880628523

    APA Style (7th edition)

  • Yuan, Yiwen. Lasso Method with SCAD Penalty for Estimation and Variable Selection in Sequential Models. 2024. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1720005880628523.

    MLA Style (8th edition)

  • Yuan, Yiwen. "Lasso Method with SCAD Penalty for Estimation and Variable Selection in Sequential Models." Doctoral dissertation, Bowling Green State University, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1720005880628523

    Chicago Manual of Style (17th edition)

bgsu1720005880628523
92
© 2024, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.