Ridge Parameter Research Articles

Quantile-based robust Kibria–Lukman estimator for linear regression model to combat multicollinearity and outliers: Real life applications using T20 cricket sports and anthropometric data

The performance of ordinary least squares (OLS) and ridge regression (RR) are influenced when outliers are present in y-direction with multicollinearity among independent variables. The robust RR with ridge parameters provides a biased estimator that has a smaller variance than conventional OLS and RR estimators. The optimal value of the ridge parameter has a vital role in bias-variance tradeoff. This study proposes quantile-based estimation of ridge parameter in robust RR to deal with the joint issue of y-direction outliers and multicollinearity. The effectiveness of the proposed estimators is evaluated using intensive Monte Carlo simulation and two real data sets in terms of mean square error (MSE) and predictions sum of squared error (PSSE) criterion. Simulation findings reveal that the newly developed estimators of ridge parameter in robust RR have better performance than OLS, RR, and existing robust RR estimators when errors are normally and non-normally distributed. The results from two numerical examples of T20 Cricket sports and anthropometric data show that the new estimator with quantile probability 0.50 and 0.99 respectively has winning performance among all competing and proposed estimators.

A ridge estimation method for the Waring regression model: simulation and application

This study focuses on parameter estimation in the presence of multicollinearity for the count response that follows the Waring distribution. The Waring regression model deals with over-dispersion. So, this study proposed the Waring ridge regression (WRR) model as a solution for multicollinearity with over-dispersion. We conducted a theoretical comparison between the ridge estimator and the maximum likelihood estimators using matrix and scalar mean squared error as a performance evaluation criterion. Several ridge parameters are considered for the WRR estimator. The performance of these parameters is numerically evaluated using a Monte Carlo simulation study and a real application. The results of the simulation and application demonstrate the superiority of the WRR model with different ridge parameters over the maximum likelihood estimator.

Design and Experiment of an Independent Leg-Type Chassis Vehicle Attitude Adjustment System

In response to the current low work efficiency of soil ridge-working machinery, as well as its poor stability, passability, and adaptability, this paper designs an independent leg-type working platform that can autonomously adjust its vehicle attitude through LiDAR scanning in a soil ridge-working environment. The platform, in terms of its mechanism and structural design, adopts dual parallelogram mechanisms, dual lead screw mechanisms, and independent column leg mechanisms, with a maximum adjustable ground clearance of 107 mm and a maximum wheelbase adjustment of 150 mm. A gyroscope is mounted at the center of the platform for attitude adjustment, ensuring the accurate data collection of the ultrasonic ranging module. Moreover, the platform adopts an adaptive adjustment method based on vehicle attitude and soil ridge shape parameters, obtaining soil ridge parameters through LiDAR and combining ultrasonic ranging module data with stepper motor pulse signals to obtain the absolute vehicle attitude parameters, using first and second linear regression methods to adjust the vehicle attitude and other working parameters. A prototype was also created, and the test data from the soil obtained through experiments show that, after leveling with the gyroscope leveling algorithm, the average value of the pitch angle is up to 0.6154°, and the average value of the roll angle is up to 0.9989°, with the maximum variance of the pitch angle being 0.0474° and the maximum variance of the tilt angle being 0.1320°. After the ultrasonic ranging module data are filtered by the Kalman filter, the maximum variance is 0.0304, and after applying the final fusion algorithm, the maximum variance is only 0.0085. The LiDAR measurement width value deviates from the actual width value by no more than 1.0 cm, and the LiDAR measurement height value deviates from the actual height value by no more than 1.0 cm. The platform’s actual adjusted width deviates from the actual soil ridge width by no more than 2.0 cm, and the platform’s actual adjusted height deviates from the actual soil ridge height by no more than 1.2 cm. This platform can improve the passability, adaptability, and stability of agricultural machinery in soil ridge work and provide technical references for subsequent related research.

A new ridge type estimator and its performance for the linear regression model: Simulation and application

Ridge regression is employed to address the issue of multicollinearity among independent variables. The shrinkage parameter (k) plays a key role in balancing the bias and variance tradeoff. This paper reviewed several promising existing ride regression estimators designed for estimating the ridge or shrinkage parameter k within the Gaussian linear regression model. In addition, we have proposed a new estimator (CK), which is a function of number of independent variables, sample size and standard error of regression model. The performance of our proposed estimator with OLS and existing shrinkage estimators, is compared using extensive Monte Carlo simulations in terms of minimum mean squared error (MSE). Simulation results demonstrated that the proposed CK estimator outperformed other in the majority of the considered simulation scenarios. A real-life data is analyzed to illustrate the findings of the paper.

How well do ridge parameter estimators proposed so far perform in terms of normality, outlier detection, and MSE criteria?

Ridge regression is a commonly used prediction method in cases of multicollinearity among regressors in multiple linear regression model. In this study, the performances of 366 different estimators proposed in the literature for ridge parameter estimation were evaluated. The criteria of estimators’ ratio of generating outliers and the proportion of normality besides the Mean Square Error (MSE) criterion were used for diagnosing ridge parameter estimators. Besides, the effect of outliers and deviations from normality generated by the ridge parameter estimators on the MSE was revealed by Spearman’s Rho correlation analysis. To do so, a Monte Carlo simulation was designed for 2420 different cases, considering the simulation parameters comprehensively in terms of the number of regressors, sample size, collinearity level and error variances. The results revealed that some ridge parameter estimators recommended according to MSE criterion, do not perform well in terms of outlier generation and normality criteria. Significant inter-linear correlations were also found among the ridge parameter estimators’ MSE performance criterion, ratios of outlier generation criterion and normality criterion. Thus, it is suggested that an effective ridge parameter estimator should perform well in terms of outlier generation and normality criteria, as well as having small MSE value.

EM algorithm for generalized Ridge regression with spatial covariates

AbstractThe generalized Ridge penalty is a powerful tool for dealing with multicollinearity and high‐dimensionality in regression problems. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given covariance matrix. The covariance matrix controls the structure of the coefficients, which depends on the particular application. For example, it is appropriate to assume that the coefficients have a spatial structure when the covariates are spatially correlated. This study proposes an Expectation‐Maximization algorithm for estimating generalized Ridge parameters whose covariance structure depends on specific parameters. We focus on three cases: diagonal (when the covariance matrix is diagonal with constant elements), Matérn, and conditional autoregressive covariances. A simulation study is conducted to evaluate the performance of the proposed method, and then the method is applied to predict ocean wave heights using wind conditions.

Development of Ridge Ensemble Standardized Drought Index (RESDI) for improving drought characterization and future assessment.

Global warming upsets the environmental balance and leads to more frequent and severe climatic events. These extreme events include floods, droughts, and heatwaves. These widespread extreme events disrupt various sectors of ecosystems directly. However, among all these events, drought is one of the most prolonged climatic events that significantly destroys the ecosystem. Therefore, accurate and efficient assessment of droughts is necessary to mitigate their detrimental impacts. In recent years, several drought indices based on global climate models (GCMs) of Coupled Model Intercomparison Project Phase 6 (CMIP6) have been proposed to quantify and monitor droughts. However, each index has its advantages and limitations. As each index ensembles different models by using different statistical approaches, it is well known that the margin of error is always a part of statistics. Therefore, this study proposed a new drought index to reduce the uncertainty involved in the assessment of droughts. The proposed index named the Ridge Ensemble Standardized Drought Index (RESDI) is based on the innovative ensemble approach termed ridge parameters and distance-based weighting (RDW) scheme. And the development of this RDW scheme is based on two types of methods i.e., ridge regression and divergence-based method. In this research, we ensemble 18 different GCMs of CMIP6 using the RDW scheme. A comparative analysis of the RDW scheme is performed against the simple model average (SMA) and Bayesian model averaging (BMA) schemes at 32 locations on the Tibetan plateau. The comparison revealed that RDW has less mean absolute error (MAE) and root-mean-square error (RMSE). Therefore, the developed RESDI based on RDW is used to project drought properties under three distinct shared socioeconomic pathway (SSP) scenarios: SSP1-2.6, SSP2-4.5, and SSP5-8.5, across seven different time scales (1, 3, 7, 9, 12, 24, and 48). The projected data is then standardized by using the K-components Gaussian mixture model (K-CGMM). In addition, the study employs steady-state probabilities (SSPs) to determine the long-term behavior of drought. The outcome of this research shows that "normal drought (ND)" has the highest probability of occurrence under all scenarios and time scales.

Airborne Radar Space–Time Adaptive Processing Algorithm Based on Dictionary and Clutter Power Spectrum Correction

Sparse recovery space–time adaptive processing (SR-STAP) technology improves the moving target detection performance of airborne radar. However, the sparse recovery method with a fixed dictionary usually leads to an off-grid effect. This paper proposes a STAP algorithm for airborne radar based on dictionary and clutter power spectrum joint correction (DCPSJC-STAP). The algorithm first performs nonlinear regression in a non-stationary clutter environment with unknown yaw angles, and it corrects the corresponding dictionary for each snapshot by updating the clutter ridge parameters. Then, the corrected dictionary is combined with the sparse Bayesian learning algorithm to iteratively update the required hyperparameters, which are used to correct the clutter power spectrum and estimate the clutter covariance matrix. The proposed algorithm can effectively overcome the off-grid effect and improve the moving target detection performance of airborne radar in actual complex clutter environments. Simulation experiments verified the effectiveness of this algorithm in improving clutter estimation accuracy and moving target detection performance.

Simulation investigations of an efficient L-band bi-frequency MILO with ridged-disk-loaded interaction structure

This article presents simulation studies of an L-band bi-frequency magnetically insulated line oscillator for its efficiency enhancement using a ridged-disk-loaded radio frequency (RF) interaction structure. The electromagnetic (EM) properties of the RF interaction structure implemented with conventional and ridged disk have been investigated with the aid of CST microwave studio suite. A comparative study between the EM properties of conventional slow-wave structures and ridged-slow-wave structures (RSWS) is presented. The impact of adding ridges at the tip of disks has been examined for its influence on the dispersion curve, phase velocity, and coupling impedance. The coupling impedance of the RSWS with ridged-disk-loaded vanes was found to be greater than that of the conventional SWS. Furthermore, influence on output power of the device is observed for different ridge's parameters. With the optimum dimension of ridge parameters, particle-in-cell simulation detects an high-power microwave at frequencies of 1.20 and 1.40 GHz, producing 3.8 GW of cumulative peak RF power with a conversion efficiency of 23.8%, when operated with a 420 kV input DC voltage and current of 38 kA.

Bootstrap-quantile ridge estimator for linear regression with applications.

Bootstrap is a simple, yet powerful method of estimation based on the concept of random sampling with replacement. The ridge regression using a biasing parameter has become a viable alternative to the ordinary least square regression model for the analysis of data where predictors are collinear. This paper develops a nonparametric bootstrap-quantile approach for the estimation of ridge parameter in the linear regression model. The proposed method is illustrated using some popular and widely used ridge estimators, but this idea can be extended to any ridge estimator. Monte Carlo simulations are carried out to compare the performance of the proposed estimators with their baseline counterparts. It is demonstrated empirically that MSE obtained from our suggested bootstrap-quantile approach are substantially smaller than their baseline estimators especially when collinearity is high. Application to real data sets reveals the suitability of the idea.

New ridge parameter estimators for the quasi-Poisson ridge regression model

The quasi-Poisson regression model is used for count data and is preferred over the Poisson regression model in the case of over-dispersed count data. The quasi-likelihood estimator is used to estimate the regression coefficients of the quasi-Poisson regression model. The quasi-likelihood estimator gives sub-optimal estimates if regressors are highly correlated—multicollinearity issue. Biased estimation methods are often used to overcome the multicollinearity issue in the regression model. In this study, we explore the ridge estimator for the quasi-Poisson regression model to mitigate the multicollinearity issue. Furthermore, we propose various ridge parameter estimators for this model. We derive the theoretical properties of the ridge estimator and compare its performance with the quasi-likelihood estimator in terms of matrix and scalar mean squared error. We further compared the proposed estimator numerically through a Monte Carlo simulation study and a real-life application. We found that both the simulation and application results show the superiority of the ridge estimator, particularly with the best ridge parameter estimator, over the quasi-likelihood estimator in the presence of multicollinearity issue.

A compensation method of carrier magnetic interference under pathological conditions for geomagnetic navigation

Geomagnetic navigation has become a hot spot in current research because of its characteristics of passiveness and good concealment. However, the magnetic interference from various ferromagnetic substances, electronic equipment, etc., of the carrier will be superimposed on the geomagnetic field, causing magnetometer measurement errors, thus affecting navigation accuracy. In practice, due to the limited maneuverability of the carrier, sufficient geomagnetic observation data cannot be obtained, resulting in the observation equation used for carrier magnetic interference compensation to be seriously pathological. To achieve the compensation of carrier magnetic interference, this paper proposes the total least squares method based on the ridge regression using the L curve to solve ridge parameters. This method can effectively suppress the measurement noise that exists on both sides of the observation equation, and is suitable for alleviating the pathological effects of carrier magnetic interference compensation. Experimental results show that the compensated magnetometer measurement error is reduced to 3% of the carrier magnetic interference by using the method proposed in this paper, which obtains more stable and accurate parameter estimates.

A new modified biased estimator for Zero inflated Poisson regression model

Zero-inflated Poisson (ZIP) model is widely used for counting data with excessive zeroes. The multicollinearity is the common factor in the explanatory variables of the count data. In this context, typically, maximum likelihood estimation (MLE) generates unsatisfactory results due to inflation of mean square error (MSE). In the solution of this problem usually, ridge parameters are used. In this study, we proposed a new modified zero-inflated Poisson ridge regression model to reduce the problem of multicollinearity. We experimented within the context of a specified simulation strategy and recorded the behavior of proposed estimators. We also apply our proposed estimator to the real-life data set and explore how our proposed estimators perform well in the presence of multicollinearity with the help of ZIP model for count data.

An investigation on the application of Ridge regression model in the optimization of virtual practice teaching innovation path of Civics and Politics courses in colleges and universities

Abstract Civic and political affairs course is a key course for colleges and universities to implement the fundamental task of cultivating people with moral character, and the rapid development of network technology and the information age has had a direct impact on the Civic and political affairs course in colleges and universities. This paper puts forward the optimization path of virtual practice teaching for Civic and Political Science courses in colleges and universities from three aspects: establishing a virtual simulation practice teaching website for Civic and Political Science courses in colleges and universities, constructing a virtual simulation practice teaching information resource base for Civic and Political Science courses and optimizing the content system of virtual simulation practice teaching for Civic and Political Science courses. In order to verify the effect of virtual practice teaching, this paper proposes a new determination method as well as a Ridge regression model for the selection of Ridge parameter K in the Ridge trace method by analyzing the existence of Ridge parameter K and the excellence of Ridge estimation. The Ridge regression model was used to examine the impact of virtual teaching on college Civics and Politics classes and found that the standardized regression coefficient beta for the virtual teaching environment is 0.113, showing significant performance. For the virtual practice teaching of Civic and Political Science classes in colleges and universities, the better the virtual teaching environment is, the better the classroom learning effect.

A new Bayesian ridge estimator for logistic regression in the presence of multicollinearity

This research introduces the Bayesian schemes for estimating logistic regression parameters in the presence of multicollinearity. The Bayesian schemes involve the introduction of a prior together with the likelihood which resulted in the posterior distribution that is not tractable, hence the use of a numerical method i.e Gibbs sampler. Different levels of multicollinearity were chosen to be p = 0.80‚0.85‚0.90‚0.95‚0.99and 0.999to accommodate severe, very severe and nearly perfect state of multicollinearity with sample sizes taken as 10,20,30,50,100,200,300 and 500.Different ridge parameters k were introduced to remedy the effect of multicollinearity .The explanatory variables used were 3 and 7. Model estimation was carried out using Bayesian approach via the Gibbs sampler of Markov Chain Monte Carlo Simulation. The means square error MSE of Bayesian logistic regression estimation was compared with the frequentist methods of the estimation. The result shows a minimum mean square error with the Bayesian scheme compared to the frequentist method.

A new robust ridge parameter estimator having no outlier and ensuring normality for linear regression model

In order to accurately estimate the regression coefficients in a multiple linear regression model having multicollinearity, ridge regression is a well-liked biased estimation technique used as an alternative to the least squares method. So far, numerous estimators have been proposed for ridge parameter estimation in the ridge regression method. In this study, a robust ridge parameter estimator that performs better than the 366 different ridge parameter estimators proposed in the literature to date has been developed using the "search method". In contrast to the studies in the literature, in addition to the Mean Square Error (MSE) criterion both the estimators and the developed robust ridge parameter estimator have been assessed in terms of outliers and normality. Furthermore, a simulation design with a total of 6050 cases were included in the study which corresponds to parameter values that varied widely in terms of the number of independent variables (p), sample size (n), correlation coefficient between independent variables (ρ), and standard deviation of errors (σ). Significant inter linear associations among the MSE, outlier detection and normality criteria were found. Results from the conducted simulation study revealed that the proposed robust ridge parameter estimator was the most effective one in terms of these three criteria, regardless of the number of regressors, sample size, multicollinearity level, and standard deviation of errors.

Evaluation and Improvement of the Method for Selecting the Ridge Parameter in System Differential Response Curves

The selection of an appropriate ridge parameter plays a crucial role in ridge estimation. A smaller ridge parameter leads to larger residuals, while a larger ridge parameter reduces the unbiasedness of the estimation. This paper proposes a constrained L-curve method to accurately select the optimal ridge parameter. Additionally, the constrained L-curve method, traditional L-curve method, and ridge trace method are individually coupled with the system differential response curve to update the streamflow in the Jianyang Basin using the SWAT model. Multiple evaluation criteria are employed to analyze the efficacy of the three methods for correction. The results demonstrate that the constrained L-curve method accurately identifies the optimal ridge parameter in the actual model. Furthermore, the coupling of the constrained L-curve method with the system differential response curve exhibits markedly superior accuracy of simulated streamflow compared to the traditional L-curve and ridge trace methods, with the mean Nash–Sutcliffe efficiency (NSE) improving from 0.71 to 0.88 after correction. The constrained L-curve method, which incorporates the physical interpretation of the estimated parameters, effectively identifies the optimal ridge parameter in practical scenarios. As a result, it demonstrates superior usability and applicability when compared to the traditional L-curve method.

Research on the role of psychological education in college Civic Education under the background of Internet

Abstract Psychological education in colleges and universities can inject new vitality into Civic Education. In this paper, the ridge estimation of regression parameters is based on the linear regression model, the canonical form of ridge regression is constructed, and the selection method of ridge parameters is proposed by combining the ridge trace plot and the Mcdorard-Garaneau method. The prediction accuracy of the ridge regression is optimized by using the idea of partial least squares for the shortcomings of the general ridge regression. After completing the improvement of ridge regression, the quantitative evaluation indexes of psychological education and Civic Education in colleges and universities were established, and the influence of psychological education on Civic Education was studied through regression analysis. The correlation coefficient R of faculty and hardware construction of psychological education on the content richness of Civic Education reached 0.725, and the standardized regression coefficient T of the former was −0.357, while the latter was −4.257, and the former was more significant than the latter. Meanwhile, the regression coefficients of organizational management and institutional setting, faculty construction and work organization and effectiveness on the level of college students’ psychological education were 0.54, 0.26 and 0.24, respectively, with significant joint effects. This study realizes the quantitative analysis of psychological education influencing Civic Education, which helps to promote the integration and development of psychological education and Civic Education.

Study of Regularized Generalized Structured Component Analysis to Overcome Multicollinearity in Component-Based SEM

Multicollinearity is one of the issues that may arise in the analysis of Structural Equation Modeling (SEM). An indication of multicollinearity is the high correlation between latent variables and the correlation between indicators forming the latent construct. Multicollinearity causes the interpretation of SEM analysis to be inappropriate. In this study, Regularized generalized structured component analysis (RGSCA) is used as a solution to overcome multicollinearity in component-based SEM. The research aims to apply RGSCA to East Java poverty data, which contains multicollinearity. The first step is analyze data using GSCA, however the weights of and indicators are not significant, and the three estimated path coefficients are also not significant at the 95% confidence interval. The high correlation value between the indicators further indicates the presence of multicollinearity. Futhermore, the data are analyzed using RGSCA with ridge parameters namely which provides minimum prediction error (CV). The results of the analysis reveal that all estimation of loading factors, weights and path coefficients are significant at 95% confidence intervals. The interpretation of the path coefficient results suggests that education, health, and economy significantly influence poverty, while health and economy also have a significant effect on education, and health additionally exhibits a significant effect on economy. The overall model evaluation results obtained a FIT value of 0.662, indicating that the model can explain about 66.2% of the data variation.

Pengujian pada Regresi Ridge dan Penerapannya terhadap Data Produk Domestik Regional Bruto Provinsi Jawa Barat

Abstract. Ridge regression is one of the methods used to stabilize the value of the regression coefficient caused by multicollinearity. In ridge regression, to reduce the impact of multicollinearity is carried out by adding ridge parameter c to the hat matrix. This ridge parameter makes the regression coefficients have a smaller variance than the least squares method estimator variance. However, the ridge estimates are biased. Thus, hypothesis testing using the usual method cannot be applied to the coefficients ridge regression. Therefore Bae, et al., (2014) developed a method for testing the hypothesis of the coefficients of ridge regression. This thesis aims to apply this method to the gross regional domestic product data for West Java province in 2022. Based on the results of the research, it shows that there is a multicollinearity problem in the data, so it is modelLed using ridge regression. it was obtained The ridge regression model : . From the results of testing the hypothesis, it can be concluded that the independent variables, namely local original income (X1), general allocation funds (X2), profit sharing funds (X3), regional expenditures (X4) and labor (X5) together have a significant effect on the PDRB (Y) of West Java Province in 2022. The ridge regression model is returned to the original model .
 Abstract. Ridge regression is one of the methods used to stabilize the value of the regression coefficient caused by multicollinearity. In ridge regression, to reduce the impact of multicollinearity is carried out by adding ridge parameter c to the hat matrix. This ridge parameter makes the regression coefficients have a smaller variance than the least squares method estimator variance. However, the ridge estimates are biased. Thus, hypothesis testing using the usual method cannot be applied to the coefficients ridge regression. Therefore Bae, et al., (2014) developed a method for testing the hypothesis of the coefficients of ridge regression. This thesis aims to apply this method to the gross regional domestic product data for West Java province in 2022. Based on the results of the research, it shows that there is a multicollinearity problem in the data, so it is modelLed using ridge regression. it was obtained The ridge regression model : . From the results of testing the hypothesis, it can be concluded that the independent variables, namely local original income (X1), general allocation funds (X2), profit sharing funds (X3), regional expenditures (X4) and labor (X5) together have a significant effect on the PDRB (Y) of West Java Province in 2022. The ridge regression model is returned to the original model .