Generalized ridge estimator shrinkage estimation based on particle swarm optimization algorithm
It is well-known that in the presence of multicollinearity, the ridge estimator is an alternative to the ordinary least square (OLS) estimator. Generalized ridge estimator (GRE) is an generalization of the ridge estimator. However, the efficiency of GRE depends on appropriately choosing the shrinkage parameter matrix which is involved in the GRE. In this paper, a particle swarm optimization method, which is a metaheuristic continuous algorithm, is proposed to estimate the shrinkage parameter matrix. The simulation study and real application results show the superior performance of the proposed method in terms of prediction error.
- Research Article
- 10.33899/iqjoss.2020.167387
- Dec 1, 2020
- IRAQI JOURNAL OF STATISTICAL SCIENCES
It is well-known that in the presence of multicollinearity, the ridge estimator is an alternative to the ordinary least square (OLS) estimator. Generalized ridge estimator (GRE) is an generalization of the ridge estimator. However, the efficiency of GRE depends on appropriately choosing the shrinkage parameter matrix which is involved in the GRE. In this paper, a particle swarm optimization method, which is a metaheuristic continuous algorithm, is proposed to estimate the shrinkage parameter matrix. The simulation study and real application results show the superior performance of the proposed method in terms of prediction error.
- Research Article
- 10.14419/ijasp.v8i1.30565
- May 15, 2020
- International Journal of Advanced Statistics and Probability
It is well-known that in the presence of multicollinearity, the Liu estimator is an alternative to the ordinary least square (OLS) estimator and the ridge estimator. Generalized Liu estimator (GLE) is a generalization of the Liu estimator. However, the efficiency of GLE depends on appropriately choosing the shrinkage parameter matrix which is involved in the GLE. In this paper, a particle swarm optimization method, which is a metaheuristic continuous algorithm, is proposed to estimate the shrinkage parameter matrix. The simulation study and real application results show the superior performance of the proposed method in terms of prediction error.  Â
- Conference Article
1
- 10.1109/iciea.2018.8397720
- May 1, 2018
With the development towards high-speed, high-capacity, high-density networking of high-speed railway, harmonic problems caused by high-speed locomotives are getting more and more serious, which has been a great threaten to the safety and stability of power system operation. The way of elimination on the influence of railway becomes increasingly important. Due to the diseconomy to install passive filters around the whole power grid, this paper presents a harmonic suppression method using the optimal configuration of passive power filter based on particle swarm optimization (PSO) method in the power grid affected by the electrified railways. At first, this paper makes an evaluation on the impacts on power system with railway both in theory and the data measured by PQView software. It makes an introduction and analysis on the methods of harmonic suppression affected by electrified railways on the power grid, and the importance of harmonic governance affected by electrified railways on the power grid was emphasized. Then, it makes a detail analysis on the theory of harmonic suppression using passive power filter based on PSO method affected by electrified railways on the power grid. Besides, according to the characteristic of Taotang power grid (Taotang power grid is an actual area network affected by the electrified railways) and the influence of harmonics on the Taotang power grid, a mathematical model is built considering the economy and effect of passive filters as the optimal objective. Then, an optimal configuration of passive filters in the Taotang power grid is given through optimizing by the PSO algorithm. Besides, the simulations and analysis are provided, and by comparing the harmonic data before the harmonic suppression using passive filters based on PSO method with the harmonic data after the optimal configuration of passive filters based on PSO algorithm, it is showed that the optimal configuration of passive power filter based on particle swarm optimization (PSO) algorithm has obvious effect on the harmonic suppression and the proposed method is validity, which provides a theoretical and engineering reference for the improvement of the harmonic in power network affected by electrified railways.
- Research Article
2
- 10.1088/1742-6596/1897/1/012019
- May 1, 2021
- Journal of Physics: Conference Series
The ridge estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The negative binomial regression model (NBRM) is a well-known model in application when the response variable is a count data with overdispersion. However, it is known that the variance of maximum likelihood estimator (MLE) of the NBRM coefficients can negatively affected in the presence of multicollinearity. In this paper, the generalized ridge estimator is proposed to overcome the limitation of ridge estimator. Several methods for estimating the shrinkage matrix have been adapted. Our Monte Carlo simulation results suggest that the proposed estimator, regardless the type of estimating method of shrinkage matrix is better than the MLE estimator and ridge estimator, in terms of MSE. In addition, some estimating method of shrinkage matrix can bring significant improvement relative to others.
- Research Article
1
- 10.3390/axioms14070527
- Jul 10, 2025
- Axioms
Predictive regression models often face a common challenge known as multicollinearity. This phenomenon can distort the results, causing models to overfit and produce unreliable coefficient estimates. Ridge regression is a widely used approach that incorporates a regularization term to stabilize parameter estimates and improve the prediction accuracy. In this study, we introduce four newly modified ridge estimators, referred to as RIRE1, RIRE2, RIRE3, and RIRE4, that are aimed at tackling severe multicollinearity more effectively than ordinary least squares (OLS) and other existing estimators under both normal and non-normal error distributions. The ridge estimators are biased, so their efficiency cannot be judged by variance alone; instead, we use the mean squared error (MSE) to compare their performance. Each new estimator depends on two shrinkage parameters, k and d, making the theoretical analysis complex. To address this, we employ Monte Carlo simulations to rigorously evaluate and compare these new estimators with OLS and other existing ridge estimators. Our simulations show that the proposed estimators consistently minimize the MSE better than OLS and other ridge estimators, particularly in datasets with strong multicollinearity and large error variances. We further validate their practical value through applications using two real-world datasets, demonstrating both their robustness and theoretical alignment.
- Research Article
8
- 10.1016/j.cmpb.2021.105933
- Jan 9, 2021
- Computer Methods and Programs in Biomedicine
Particle swarm optimizer for arterial blood flow models
- Research Article
3
- 10.3390/sym16020223
- Feb 12, 2024
- Symmetry
Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to non-uniform shrinkage; this was shown to perform well in sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (first version published on 7 December 2023) that implements both the ridge estimator and generalized ridge estimator. The package is equipped with generalized cross-validation for the automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on the R package “glmnet”. Hence the generalized ridge estimator may be the most recommended estimator for sparse and high-dimensional models. We demonstrate the package using intracerebral hemorrhage data.
- Research Article
3
- 10.17485/ijst/2016/v9i45/101915
- Dec 20, 2016
- Indian Journal of Science and Technology
Background/Objectives: PV array being shaded partially by buildings, trees or passing clouds is common. This makes the P-V curve of the PV system complex with more than one peak. MPPT algorithm capable of consistently detecting the global peak within a short duration of time is essential. Methods/Statistical Analysis: Lately Particle Swarm Optimization (PSO) algorithm has been used for Maximum Power Point (MPP) tracking due to its ability to locate the MPP irrespective of its location in the P-V curve. This paper evaluates and compares the performance of the basic PSO algorithm and the modified PSO algorithms for ten different shading patterns. Findings: The basic PSO algorithm is compared with three modified PSO algorithms - PSO algorithm with random numbers eliminated, PSO algorithm with linearly varying constants and PSO algorithm with fixed maximum iterations. The basic PSO algorithm gives good results but random numbers in the algorithm tends to make the convergence time random for the same shading pattern and makes hardware implementation difficult. The PSO algorithm with random numbers eliminated overcomes this disadvantage and is found to give good results. But the convergence time is a little higher and varies with shading pattern. The PSO algorithm with fixed maximum iterations gives good performance with shorter and fixed convergence time. Application/Improvements: PSO algorithm with fixed maximum iterations thus improves the responsiveness of the algorithm to rapidly changing patterns of shading. Keywords: Maximum Power Point Tracking, Partial Shading, Particle Swarm Optimization, PV Array
- Research Article
3
- 10.1049/iet-map.2015.0169
- Feb 1, 2016
- IET Microwaves, Antennas & Propagation
This study presents wideband analytical Green's functions of microstrip structures using a two‐dimensional (2D) complex images method. The unknown coefficients of exponential terms are obtained using different particle swarm optimisation (PSO) algorithms such standard PSO, meta PSO, binary PSO, quantum PSO (QPSO) and ramped convergence PSO (RCPSO). The simulation results of both the magnetic vector and electric scalar potentials obtained by the PSO methods are compared and discussed. It is shown that the QPSO and RCPSO methods give considerably better solutions to the problem compared with other PSO algorithms. Then, a hybrid QPSO‐gradient‐based technique is used to improve the precision of the 2D complex images. The closed‐form Green's functions are valid over a wide range of frequencies and regions. The numerical results show close agreement with the rigorous numerical integration of Sommerfeld integrals.
- Research Article
32
- 10.3901/cjme.2014.0527.302
- Sep 1, 2014
- Chinese Journal of Mechanical Engineering
The active magnetic bearing(AMB) suspends the rotating shaft and maintains it in levitated position by applying controlled electromagnetic forces on the rotor in radial and axial directions. Although the development of various control methods is rapid, PID control strategy is still the most widely used control strategy in many applications, including AMBs. In order to tune PID controller, a particle swarm optimization(PSO) method is applied. Therefore, a comparative analysis of particle swarm optimization(PSO) algorithms is carried out, where two PSO algorithms, namely (1) PSO with linearly decreasing inertia weight(LDW-PSO), and (2) PSO algorithm with constriction factor approach(CFA-PSO), are independently tested for different PID structures. The computer simulations are carried out with the aim of minimizing the objective function defined as the integral of time multiplied by the absolute value of error(ITAE). In order to validate the performance of the analyzed PSO algorithms, one-axis and two-axis radial rotor/active magnetic bearing systems are examined. The results show that PSO algorithms are effective and easily implemented methods, providing stable convergence and good computational efficiency of different PID structures for the rotor/AMB systems. Moreover, the PSO algorithms prove to be easily used for controller tuning in case of both SISO and MIMO system, which consider the system delay and the interference among the horizontal and vertical rotor axes.
- Research Article
11
- 10.1108/imds-02-2018-0063
- Oct 31, 2018
- Industrial Management & Data Systems
PurposeThe purpose of this paper is to develop a novel intuitionistic fuzzy seasonality regression (IFSR) with particle swarm optimization (PSO) algorithms to accurately forecast air pollutions, which are typical seasonal time series data. Seasonal time series prediction is a critical topic, and some time series data contain uncertain or unpredictable factors. To handle such seasonal factors and uncertain forecasting seasonal time series data, the proposed IFSR with the PSO method effectively extends the intuitionistic fuzzy linear regression (IFLR).Design/methodology/approachThe prediction model sets up IFLR with spreads unrestricted so as to correctly approach the trend of seasonal time series data when the decomposition method is used. PSO algorithms were simultaneously employed to select the parameters of the IFSR model. In this study, IFSR with the PSO method was first compared with fuzzy seasonality regression, providing evidence that the concept of the intuitionistic fuzzy set can improve performance in forecasting the daily concentration of carbon monoxide (CO). Furthermore, the risk management system also implemented is based on the forecasting results for decision-maker.FindingsSeasonal autoregressive integrated moving average and deep belief network were then employed as comparative models for forecasting the daily concentration of CO. The empirical results of the proposed IFSR with PSO model revealed improved performance regarding forecasting accuracy, compared with the other methods.Originality/valueThis study presents IFSR with PSO to accurately forecast air pollutions. The proposed IFSR with PSO model can efficiently provide credible values of prediction for seasonal time series data in uncertain environments.
- Research Article
11
- 10.1016/j.heliyon.2021.e08247
- Oct 1, 2021
- Heliyon
Collaborative beamforming in wireless sensor networks using a novel particle swarm optimization algorithm variant
- Research Article
32
- 10.12989/sem.2014.51.4.547
- Aug 25, 2014
- Structural Engineering and Mechanics
This study focuses on the application of an active tuned mass damper (ATMD) for controlling the seismic response of an 11-story building. The control action is achieved by combination of a fuzzy logic controller (FLC) and Particle Swarm Optimization (PSO) method. FLC is used to handle the uncertain and nonlinear phenomena while PSO is used for optimization of FLC parameters. The FLC system optimized by PSO is called PSFLC. The optimization process of the FLC system has been performed for an 11-story building under the earthquake excitations recommended by International Association of Structural Control (IASC) committee. Minimization of the top floor displacement has been used as the optimization criteria. The results obtained by the PSFLC method are compared with those obtained from ATMD with GFLC system which is proposed by Pourzeynali et al. and non-optimum FLC system. Based on the parameters obtained from PSFLC system, a global controller as PSFLCG is introduced. Performance of the designed PSFLCG has been checked for different disturbances of far-field and near-field ground motions. It is found that the ATMD system, driven by FLC with the help of PSO significantly reduces the peak displacement of the example building. The results show that the PSFLCG decreases the peak displacement of the top floor by about 10%-30% more than that of the FLC system. To show the efficiency and superiority of the adopted optimization method (PSO), a comparison is also made between PSO and GA algorithms in terms of success rate and computational processing time. GA is used by Pourzeynali et al for optimization of the similar system.
- Research Article
4
- 10.1080/02664763.2021.1895088
- Mar 16, 2021
- Journal of Applied Statistics
In this study, some shrinkage estimators using a median ranked set sample in the presence of multicollinearity were studied. Initially, we constructed the multiple regression model using median ranked set sampling. We also adapted the Ridge and Liu-type estimators to these multiple regression model. To investigate the efficiency of these estimators, a simulation study was performed for a different number of explanatory variables, sample sizes, correlation coefficients, and error variances in perfect and imperfect ranking cases. In addition, these estimators were compared with other estimators that are based on ranked set sample using simulation study. It is shown that when the collinearity is moderate, Ridge estimator using median ranked set sample performs better than other estimators and when the collinearity increases, Liu-type estimator using median ranked set sample gets better than all other estimators do. When the collinearity is smaller than 0.95, ridge estimator based on median ranked set sample is more efficient than Liu-type estimator based on same sample. However, this threshold increases as the sample size increases and the number of explanatory variables decreases. In addition, real data example is presented to illustrate how collinearity affects the estimators under median ranked set sampling and ranked set sampling.
- Research Article
4
- 10.3390/ma16051953
- Feb 27, 2023
- Materials
Designing thermal conductivity efficiently is one of the most important study fields for taking the advantages of woven composites. This paper presents an inverse method for the thermal conductivity design of woven composite materials. Based on the multi-scale structure characteristics of woven composites, a multi-scale model of inversing heat conduction coefficient of fibers is established, including a macroscale composite model, mesoscale fiber yarn model, microscale fiber and matrix model. In order to improve computational efficiency, the particle swarm optimization (PSO) algorithm and locally exact homogenization theory (LEHT) are utilized. LEHT is an efficient analytical method for heat conduction analysis. It does not require meshing and preprocessing but obtains analytical expressions of internal temperature and heat flow of materials by solving heat differential equations and combined with Fourier’s formula, relevant thermal conductivity parameters can be obtained. The proposed method is based on the idea of optimum design ideology of material parameters from top to bottom. The optimized parameters of components need to be designed hierarchically, including: (1) combing theoretical model with the particle swarm optimization algorithm at the macroscale to inverse parameters of yarn; (2) combining LEHT with the particle swarm optimization algorithm at the mesoscale to inverse original fiber parameters. To identify the validation of the proposed method, the present results are compared with given definite value, which can be seen that they have a good agreement with errors less than 1%. The proposed optimization method could effectively design thermal conductivity parameters and volume fraction for all components of woven composites.
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