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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Ridge Regression Method and Bayesian Estimators under Composite LINEX Loss Function to Estimate the Shape Parameter
Mansour F Yassen1, Fuad S Al-Duais1, Mohammed M A Almazah2
1Mathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Al Aflaj, Saudi Arabia.
Computational Intelligence and Neuroscience
|September 8, 2022
Summary
This study introduces Ridge Regression for estimating the Lomax distribution shape parameter. Ridge Regression shows promising performance, outperforming Ordinary Least Squares in simulations.
Area of Science:
- Statistics
- Probability Distributions
Background:
- The Lomax distribution is frequently used in reliability and survival analysis.
- Accurate estimation of its shape parameter is crucial for model performance.
Purpose of the Study:
- To evaluate the Ridge Regression method for estimating the Lomax distribution shape parameter.
- To compare Ridge Regression with classical and Bayesian estimation approaches.
Main Methods:
- Ridge Regression was applied to estimate the Lomax distribution shape parameter.
- Classical estimators (Maximum Likelihood, Ordinary Least Squares, etc.) and Bayesian estimators with various loss functions (Squared Error, Linear Exponential, Composite Linear Exponential) were used for comparison.
- Monte Carlo simulations were conducted to assess performance using Mean Square Error (MSE).
Main Results:
- Ridge Regression demonstrated promising results for estimating the Lomax distribution shape parameter.
- The Ridge Regression method exhibited superior performance compared to the Ordinary Least Squares method.
- Simulations indicated the potential applicability of Ridge Regression in real-world scenarios.
Conclusions:
- Ridge Regression is a viable and effective method for estimating the Lomax distribution shape parameter.
- The study highlights the advantages of Ridge Regression over traditional methods like Ordinary Least Squares in specific contexts.
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