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This study aimed to build a valid model to predict maximal weightlifting competition performance using ordinary least squares linear regression (OLR) and penalized (Ridge) linear regression (penLR) in 29 elite male weightlifters. One repetition maximum (1RM) or 3RM test results of assistant exercises were used as predictors. Maximal performance data of competition and assistant exercises were collected during a macrocycle in preparation for a competition. One repetition maximum snatch pull, 3RM back squat, 1RM overhead press, and body mass were used to predict the 1RM snatch; and 1RM clean pull, 3RM front squat, 1RM overhead press, and body mass were used to predict the 1RM clean and jerk. Model validation was performed using cross-validation (CV) and external validation (EV; random unknown dataset) for the coefficient of determination and root mean square error (RMSE). Results revealed that penLR models present more plausible output in the relative importance of highly correlated predictors. Of note, the 1RM snatch pull is the most relevant predictor for the 1RM snatch, whereas the 1RM clean pull and 3RM front squat are the most relevant predictors for the 1RM clean and jerk. Validation-based absolute predictive error (RMSE) ranged between ≈ 3-9 kg for the 1RM snatch and ≈ 3-7 kg for the 1RM clean and jerk, depending on the model (OLR vs. penLR) and validation procedure (CV vs. EV). In conclusion, penLR models should be used over OLR models to analyze highly correlated predictors because of more plausible model coefficients and smaller predictive errors. [ABSTRACT FROM AUTHOR]

Recent studies focus on modelling count data, which often shows overdispersion or underdispersion. The Conway–Maxwell–Poisson (COMP) regression model effectively handles such dispersion. However, multicollinearity can negatively impact the maximum likelihood estimator (MLE) by increasing variance. To address this, biased estimators like the ridge estimator have been suggested to mitigate multicollinearity effects. This research proposes a new COMP hybrid estimator to further address multicollinearity issues. Theoretical comparisons between the COMP hybrid estimator, MLE, and other COMP estimators reveal that the hybrid estimator reduces mean squared error. Monte Carlo simulations and practical applications confirm that these proposed estimators outperform both MLE and existing COMP estimators. [ABSTRACT FROM AUTHOR]

Ridge regression was originally proposed as an alternative to ordinary least-squares regression to address multicollinearity in linear regression and was later extended to logistic and Cox regressions. The ridge estimator is interpreted as the Bayesian posterior mean or median in the Bayesian framework when the regression coefficients have multivariate normal priors. We previously proposed using vine copula-based joint priors on regression coefficients in linear and Cox regressions, including an interaction that promotes the use of ridge regression because the interaction term can result in multicollinearity. We showed that vine copula-based priors improve the estimation accuracy over the multivariate normal prior, and they would be a promising approach in other regression types, such as logistic regression. In this study, we focus on a case involving two covariates and their interaction terms, and propose a vine copula-based prior for Bayesian ridge estimators under a logistic model. Simulation and data analysis results show that Archimedean (Clayton and Gumbel) copula priors are superior to other priors (the Gaussian copula and trivariate normal priors) in the presence of multicollinearity. [ABSTRACT FROM AUTHOR]

Climate transition zones are ecologically sensitive regions that respond to changes in complex natural conditions. Analyzing the spatiotemporal evolution trends and impact factors of landscape ecological risk is crucial for maintaining regional ecosystem security. However, research predominantly focused on the past analytical paradigm, which often needed more strategic predictions for future scenarios tailored to diverse developmental requirements. This study analyzed land use changes in the Huai River Basin during 2000, 2010, and 2020 and used the Future Land Use Simulation model to conduct a multi-scenario simulation for 2030. Subsequently, this study assessed the landscape ecological risk from 2000 to 2030 and analyzed the influencing mechanisms using the ridge regression model. The results showed that: (1) The primary transitions were concentrated between cropland and construction land. By 2030, the area of construction land was projected to continue to expand, with the greatest increase of 2906 km2 anticipated in the natural development scenario. (2) The overall spatial pattern of landscape ecological risk showed a "high in the east and low in the west" distribution, with the lowest risk areas predominating (accounting for over 43%). Over the past 20 years, the risk initially increased and then decreased, and by 2030, the risk was expected to decline further. (3) The risk exhibited significant positive spatial autocorrelation. By 2030, the constraint of spatial location on risk distribution would decrease. Local spatial clustering was mainly characterized by "Low-Low" regions (accounting for 20%). (4) Vegetation cover consistently correlated negatively with ecological risk and was the most influential factor, with relative contribution rates all exceeding 21%. The findings have provided a scientific reference for the ecological and environmental management of areas with intense human activity under complex climatic conditions. [ABSTRACT FROM AUTHOR]

Classification as an essential part of Machine Learning and Data Mining has significant roles in engineering, medicine, agriculture, military, etc. With the evolution of data collection tools and the unceasing efforts of researchers, new datasets with huge dimensions are obtained so that each data sample has multiple labels. This kind of classification is called Multi-Class Classification (MLC) and demands new techniques to predict the set of labels for a data instance. To date, a variety of methods have been proposed to solve MLC problems. However, new high-dimensional datasets with challenging patterns are being developed, making it necessary for new research to be conducted to develop more efficient methods. This paper presents a novel framework named QLHA to solve MLC problems more efficiently. In the QLHA, the Principal Label Space Transformation (PLST) and Ridge Regression (RR) are recruited to predict the labels of data. Next, an effective objective function is introduced. Also, a hybrid metaheuristic algorithm called QGTOJS is provided to optimize objective value and enhance the predicted labels by selecting the most relevant features. In the QGTOJS, the Gorilla Troops Optimization (GTO) and Jellyfish Search algorithm (JS) are binarized and hybridized through a modified variant of the Q-learning algorithm. Besides, an adjusted Hill Climbing strategy is adopted to balance the exploration and exploitation and improve local optima departure. Likewise, a local search mechanism is provided to enhance searchability as much as possible. Eventually, the QLHA is applied to ten multi-label datasets and the obtained results are compared with heuristic and metaheuristic-based MLC methods numerically and visually. The experimental results disclosed the effectiveness of the contributions and superiority of the QLHA over competitors. [ABSTRACT FROM AUTHOR]

The popularity of genomic selection as an efficient and cost-effective approach to estimate breeding values continues to increase, due in part to the significant saving in genotyping. Ridge regression is one of the most popular methods used for genomic prediction; however, its efficiency (in terms of prediction performance) depends on the appropriate tunning of the penalization parameter. In this paper we propose a novel, more efficient method to select the optimal penalization parameter for Ridge regression. We compared the proposed method with the conventional method to select the penalization parameter in 14 real data sets and we found that in 13 of these, the proposed method outperformed the conventional method and across data sets the gains in prediction accuracy in terms of Pearson's correlation was of 56.15%, with not-gains observed in terms of normalized mean square error. Finally, our results show evidence of the potential of the proposed method, and we encourage its adoption to improve the selection of candidate lines in the context of plant breeding. [ABSTRACT FROM AUTHOR]

In this article, we present the Liu estimator for the Cox proportional hazards (PH) model. The maximum partial likelihood estimator (MPLE) is commonly used for estimation of the coefficients of the Cox PH model. The MPLE performs well if the covariates are uncorrelated. However, in many situations, covariates become seriously correlated, and then the MPLE is inept to produce stable estimates for the unknown coefficients. To overcome this situation, the literature suggests using the ridge estimator as an alternative to the MPLE for the Cox PH model in the presence of multicollinearity. In the present article, we extend the Liu estimator, a popular superseder of the ridge estimator, for the Cox PH model and discuss its properties. The performance of the proposed estimator has been compared with the available estimators using the scalar mean squared error criterion through the Monte Carlo simulations. A numerical example has also been provided for the illustration. [ABSTRACT FROM AUTHOR]

Poisson and negative binomial regressions are popular methods for modelling the relationship between a count variable and explanatory variables. In the presence of multicollinearity, ridge regression is an alternative to the maximum likelihood estimation for regression coefficients. Furthermore, ridge estimators are interpreted as the Bayesian posterior mean (or mode) when the regression coefficients follow a multivariate normal prior. However, using the multivariate normal prior may not effectively estimate regression coefficients, especially in the presence of interaction terms. This study proposes vine copula-based priors for Bayesian ridge estimators in Poisson and negative binomial regression models. The simulations and data analysis results indicate that for the Poisson model with equidispersion and the negative binomial model with overdispersion, the Clayton and Gumbel copula priors of the Archimedean family achieve superior performance than the multivariate normal prior and Gaussian copula prior. [ABSTRACT FROM AUTHOR]

This study aims to model the reduction in the Tinnitus Functional Index (TFI) utilizing supervised machine learning algorithms, focusing primarily on Ordinary Least Squares (OLS), K-Nearest Neighbor (KNN), Ridge, and Lasso regressions. Our analysis highlighted Group, ISI, and SWLS as significant predictors of TFI reduction, identified through the best subset selection and confirmed by both forward and backward selection criteria in the OLS regression. Notably, the shrinkage methods, Ridge and Lasso regressions, demonstrated superior performance compared to OLS and KNN, with the Ridge regression presenting the smallest test mean square error (MSE) of 318.30. This finding establishes the Ridge regression as the best model for analyzing our Tinnitus dataset relative to the other methods, which exhibited test MSEs of 319.28 (Lasso), 330.76 (OLS), and 584.92 (KNN), respectively. This research highlights the potential of supervised machine learning algorithms in advancing personalized Tinnitus treatment, reflecting broader trends in the field as evidenced by studies in the literature. By leveraging these algorithms, we can enhance treatment precision and outcomes, contributing significantly to improved quality of life for individuals with Tinnitus. Future research should explore the integration of multimodal data and longitudinal applications of these algorithms to further refine predictive capabilities and treatment effectiveness. [ABSTRACT FROM AUTHOR]

Air pollution is defined as an adverse event that negatively affects ecosystems and standard conditions necessary for human survival and progress, manifested by certain substances in the atmosphere exceeding specific concentration levels. The control of air pollution is a significant strategic task related to the national economies and the well-being of the people. In the face of increasingly severe environmental pollution problems, accurately predicting air pollution indicators becomes crucial. Among the popular air pollution prediction methods, the K-nearest neighbors (KNN) appears to be one of most promising approaches. In this paper, we develop a novel KNN rule that combines the ridge estimators called KNN-ridge regression (KNN-RR). The proposed KNN-RR is motivated by the sensitivity problem that multi-collinearity exists in the current KNN regression, aiming to enhance the prediction performance. Our theoretical result shows that under some mild assumptions, there exists a penalty parameter such that the mean square prediction error of ridge regression is smaller than that of ordinary least square regression. We examine the empirical performances of KNN-RR and other methods on real-world datasets, such as the AQI and PM2.5 prediction, and the results indicate that our method has some advantages in improving prediction accuracy. To a certain extent, this paper paves a new way to improve some supervised machine learning methods. [ABSTRACT FROM AUTHOR]

Vegetation phenology is highly sensitive to climate change, and an examination of vegetation phenology across diverse climatic conditions is crucial for identifying key factors influencing vegetation dynamics. However, there is a significant lack of macroscopic research and quantitative assessments on the response of vegetation phenology to meteorological factors in large-scale zones. This study employed Whittaker filtering and dynamic thresholding to extract phenological parameters of vegetation in China. Trend analysis was used to investigate the spatiotemporal changes in vegetation phenology from 1982 to 2022, while partial correlation and ridge regression analysis were conducted to quantify the response of vegetation in different zones to meteorological factors. The findings of this study demonstrate that over the past four decades, the start of the growing season (SOS) of vegetation in China has progressively advanced annually, whereas the end of the growing season (EOS) has progressively delayed annually, leading to an annual increase in the length of the growing season (LOS). Notably, these changes exhibit significant spatial variations. The response of vegetation phenology to temperature and precipitation is relatively complex and is closely related to local climatic conditions, humidity, vegetation type, etc. Different zones and diverse vegetation types have very different sensitivities to the same meteorological factor, sometimes even demonstrating contrasting responses. Consequently, this study is expected to clarify the response relationship between different vegetation ecosystems and meteorological factors in large-scale areas. [ABSTRACT FROM AUTHOR]

The global shift towards electric vehicles (EVs) underscores the critical need for reliable battery performance and safety. Lithium-ion batteries, particularly Li-NMC (lithium nickel manganese cobalt oxide), are widely adopted for their balanced functional and performance characteristics. However, the advancement of batteries with higher nickel content and reduced manganese and cobalt introduces challenges, including increased susceptibility to thermal runaway and degradation, especially under abusive conditions like over-discharge. This study addresses significant research gaps by developing a machine learning (ML) algorithm for the early detection and predictive maintenance of over-discharged Li-NMC batteries. Current methods often fail to identify and mitigate the effects of continuous cycling, which can release harmful free radicals such as singlet oxygen (1 O 2 ) and superoxide ( O 2 - ) that accelerate degradation. Our ML approach utilizes supervised learning, feature engineering, and model optimization, leveraging key input features such as voltage, time, and cycle count which are derived from extensive battery life testing. To validate our model, we conducted scanning electron microscopy energy-dispersive spectroscopy (SEM–EDS), galvanostatic charge–discharge (GCD) tests, and rate capability tests. The proposed ridge regression model achieved a mean absolute error (MAE) of 0.11422%, a mean squared error (MSE) of 0.02313%, and an R-squared (R2) value of 0.99, outperforming other models such as Decision Trees (DT), Recurrent Neural Networks (RNNs), Support Vector Machines (SVMs), Gradient Boosting (GB), and Lasso Regression. Our model addresses key shortcomings of existing methods, particularly in predicting degradation in precycled batteries subjected to fault induction. The insights gained contribute to a robust control strategy for EV battery management, enabling proactive maintenance, timely battery replacement, and enhanced system reliability and safety, effectively addressing the long-term challenges in battery health management. [ABSTRACT FROM AUTHOR]

In contrast to multi-class classification, in multi-label classification (MLC), each data sample is a member of several classes. In this regard, the classifiers should discover more complex patterns within the data; accordingly, the complexity grows remarkably. Recently, scholars used the binary relevance, the label powerset, and the ensemble method (EM) techniques to extend state-of-the-art classifiers or develop new ones to solve real-world MLC problems more optimally. The current paper recruits the ridge regression (RR) and a decision tree (DT) and presents a new MLC model named PHMLC. In the PHMLC, the Laplacian Eigenmaps Nonlinear Dimensionality Reduction Algorithm is employed to omit the redundant and irrelevant features. Next, the data is encoded by the principal label space transformation (PLST) and singular value decomposition. Then, the RR is recalled to predict the first set of labels through the encoded data. Besides, the Binary Relevance technique is applied to the original DT, and an MLC model called BR-DT is introduced. The BR-DT is responsible for predicting the second set of labels. Eventually, the greedy selection mechanism is utilized to obtain final labels based on the predicted labels by the PLST-based RR and the BR-DT models. To demonstrate the PHMLC's effectiveness, the PHMLC model is applied to nine real-life multi-label datasets, and the results are compared with the BR-SVM, CPLST, BR-Ridge, BR-DR, PLST, and BR-DT models regarding the AP, EM, HS, Macro, and Micro F1 metrics. [ABSTRACT FROM AUTHOR]

Data analysis is very important in many fields of science. The most preferred methods in data analysis is linear regression due to its simplicity to interpret and ease of application. One of the assumptions accepted while obtaining linear regression is that there is no correlation between the independent variables in the model which refers to absence of multicollinearity. As a result of multicollinearity, the variance of the parameter estimates will be high and this reduces the accuracy and reliability of the linear models. Shrinkage methods aim to handle the multicollinearity problem by minimizing the variance of the estimators in linear model. Ridge Regression, Lasso, and Elastic-Net methods are applied to different simulated data sets with different characteristics and also real world data sets. Based on performance results, the methods are compared according to multi-criteria decision making method named TOPSIS, and the order of preference is determined for each data set. [ABSTRACT FROM AUTHOR]

Deep learning models, such as recurrent neural network (RNN) models, are suitable for modeling and forecasting non-stationary time series but are not interpretable. A prediction model with interpretability and high accuracy can improve decision makers' trust in the model and provide a basis for decision making. This paper proposes a double decomposition strategy based on wavelet decomposition (WD) and empirical mode decomposition (EMD). We construct a prediction model of high-order fuzzy cognitive maps (HFCM), called the WE-HFCM model, which considers interpretability and strong reasoning ability. Specifically, we use the WD and EDM algorithms to decompose the time sequence signal and realize the depth extraction of the signal's high-frequency, low-frequency, time-domain, and frequency domain features. Then, the ridge regression algorithm is used to learn the HFCM weight vector to achieve modeling prediction. Finally, we apply the proposed WE-HFCM model to stationary and non-stationary datasets in simulation experiments. We compare the predicted results with the autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) models.For stationary time series, the prediction accuracy of the WE-HFCM model is about 45% higher than that of the ARIMA, about 35% higher than that of the SARIMA model, and about 16% higher than that of the LSTM model. For non-stationary time series, the prediction accuracy of the WE-HFCM model is 69% higher than that of the ARIMA and SARIMA models. [ABSTRACT FROM AUTHOR]

The advantages and disadvantages of application of Padé approximants to regression analysis with two independent covariates are discussed. The main difficulty of using Padé function is nonlinearity of data fitting. Possible approaches to overcoming the problem are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations in case of rational functions. The possibility of using ridge regularization technique to avoid overfitting is demonstrated in this approach. To illustrate the efficiency of the suggested method, several practical cases from physics and reliability theory are considered. [ABSTRACT FROM AUTHOR]

Soccer is evolving into a science rather than just a sport, driven by intense competition between professional teams. This transformation requires efforts beyond physical training, including strategic planning, data analysis, and advanced metrics. Coaches and teams increasingly use sophisticated methods and data-driven insights to enhance decision-making. Analyzing team performance is crucial to prepare players and coaches, enabling targeted training and strategic adjustments. Expected goals (xG) analysis plays a key role in assessing team and individual player performance, providing nuanced insights into on-field actions and opportunities. This approach allows coaches to optimize tactics and lineup choices beyond traditional scorelines. However, relying solely on xG might not provide a full picture of player performance, as a higher xG does not always translate into more goals due to the intricacies and variabilities of in-game situations. This paper seeks to refine performance assessments by incorporating predictions for both expected goals (xG) and actual goals (aG). Using this new model, we consider a wider variety of factors to provide a more comprehensive evaluation of players and teams. Another major focus of our study is to present a method for selecting and categorizing players based on their predicted xG and aG performance. Additionally, this paper discusses expected goals and actual goals for each individual game; consequently, we use expected goals per game (xGg) and actual goals per game (aGg) to reflect them. Moreover, we employ regression machine learning models, particularly ridge regression, which demonstrates strong performance in forecasting xGg and aGg, outperforming other models in our comparative assessment. Ridge regression's ability to handle overlapping and correlated variables makes it an ideal choice for our analysis. This approach improves prediction accuracy and provides actionable insights for coaches and analysts to optimize team performance. By using constructed features from various methods in the dataset, we improve our model's performance by as much as 12%. These features offer a more detailed understanding of player performance in specific leagues and roles, improving the model's accuracy from 83% to nearly 95%, as indicated by the R-squared metric. Furthermore, our research introduces a player selection methodology based on their predicted xG and aG, as determined by our proposed model. According to our model's classification, we categorize top players into two groups: efficient scorers and consistent performers. These precise forecasts can guide strategic decisions, player selection, and training approaches, ultimately enhancing team performance and success. [ABSTRACT FROM AUTHOR]

Ridge regression is a variant of linear regression that aims to circumvent the issue of collinearity among predictors. The ridge parameter k has an important role in the bias-variance tradeoff. In this article, we introduce a new approach to select the ridge parameter to deal with the multicollinearity problem with different behavior of the error term. The proposed ridge estimator is a function of the number of predictors and the standard error of the regression model. An extensive simulation study is conducted to assess the performance of the estimators for the linear regression model with different error terms, which include normally distributed, non-normal and heteroscedastic or autocorrelated errors. Based upon the criterion of mean square error (MSE), it is found that the new proposed estimator outperforms OLS, commonly used and closely related estimators. Further, the application of the proposed estimator is provided on the COVID-19 data of India. [ABSTRACT FROM AUTHOR]

Enhancing marine carbon sequestration through nearshore aquaculture is a novel scientific approach to addressing global climate change and facilitating low-carbon development. Scientifically estimating the quantity and price of China's marine fisheries carbon sinks provides a crucial foundation for promoting marine carbon trading. In this article, firstly, the long-term carbon storage capacity of China's marine carbon sequestration fishery available from 1979 to 2022 for carbon trading is calculated. And then a transcendental logarithmic production function model incorporating ridge regression analysis, and an accounting equation for estimating the shadow price of China's marine fisheries carbon sequestration are established. Simultaneously, the distortion level of China's marine fisheries carbon sequestration prices from 2015 to 2022 is measured, and the reasons and economic effects of the distortion in prices are analyzed. The research results show that: 1) The capacity of a net carbon sequestration in China's marine carbon sequestration fishery for carbon trading, ranged from 78,869.01 tons in 1979 to 1,232,762.27 tons in 2022, with an average annual capacity of 592,472.07 tons and an average annual growth rate of 7.48%; 2) The price of China's marine fisheries carbon sinks increased from 39.46 CNY in 1979 to 375.96 CNY in 2022, with an average annual growth rate of 6.00%. The average annual price was 167.87 CNY; 3) There were varying degrees of distortion in China's marine fisheries carbon sequestration prices from 2015 to 2022, which decreased annually with the construction of China's own carbon trading market and the practice of trading. To realize the value of marine fisheries carbon sequestration, it is necessary to actively promote the development of voluntary emission reduction markets, develop carbon trading futures markets, and strengthen the dynamic monitoring system for resources. [ABSTRACT FROM AUTHOR]

The article examines whether expert knowledge improves the estimation results of real estate mass appraisal models. Six econometric models were compared: OLS, mixed, the Bayesian model, the Inequality Restricted Least Squares (IRLS) model, ridge and LASSO regression (with regularization). In three of the models (mixed, Bayesian, and IRLS) prior knowledge was applied. In mixed and Bayesian models priors took the form of intervals for model parameters. In IRLS, restrictions in the form of inequalities were applied. In the empirical example mass appraisal models were applied in the valuation of undeveloped land for residential purposes. Models with prior knowledge turned out to be the best with regard to the consistency of estimates with theory. Also, prediction accuracy was better for models with prior knowledge. In the case of low quality data expert knowledge might significantly improve estimation results of real estate mass appraisal econometric models. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical inference. Several authors suggest to orthogonalize both the variable of interest and the outcome with respect to the nuisance variables, and then regress the residual outcome with respect to the residual variable. This is possible if the covariance structure of the regressors is perfectly known, or is sufficiently structured that it can be estimated accurately from data (e.g. the precision matrix is sufficiently sparse). Here we consider a regime in which the covariate model can only be estimated inaccurately, and hence existing debiasing approaches are not guaranteed to work. We propose the correlation adjusted debiased Lasso , which nearly eliminates this bias in some cases, including cases in which the estimation errors are neither negligible nor orthogonal. [ABSTRACT FROM AUTHOR]

Regression analysis is one of the statistical methods used to determine the causal relationship between one or more explanatory variables to the affected variable. The problem that often occurs in regression analysis is that there are multicollonity and outliers. To deal with such problems can be solved using ridge regression analysis and robust regression. Ridge regression can solve the problem of multicollinearas by assigning a constant k to the matrix Z′Z. But in this method the resulting bias value is still high, so to overcome this problem, the jackknife ridge regression method is used. Meanwhile, to overcome outliers in the data using robust regression methods which have several estimation methods, two of which are the Generalized-M (GM) estimator and the Least Trimmed Square (LTS) estimator. The aim of the study is to solve the problem of multicollinearity and outliers simultaneously using robust jackknife ridge regression method with GM estimators and LTS estimators. The results showed that the robust ridge jackknife regression method with LTS estimator can control multicollinearity and outliers simultaneously better based on MSE, AIC and BIC values compared to the robust ridge jackknife regression method with GM estimators. This is indicated by the value MSE = -6.60371, AIC = 75.823 and BIC = 81.642 on LTS estimators that are of lower value than GM estimators.

AbstractFor grouped covariates, we propose a framework for boosting that allows for sparsity within and between groups. By using component-wise and group-wise gradient ridge boosting simultaneously with adjusted degrees of freedom or penalty parameters, a model with similar properties as the sparse-group lasso can be fitted through boosting. We show that within-group and between-group sparsity can be controlled by a mixing parameter, and discuss similarities and differences to the mixing parameter in the sparse-group lasso. Furthermore, we show under which conditions variable selection on a group or individual variable basis happens and provide selection bounds for the regularization parameters depending solely on the singular values of the design matrix in a boosting iteration of linear Ridge penalized boosting. In special cases, we characterize the selection chance of an individual variable versus a group of variables through a generalized beta prime distribution. With simulations as well as two real datasets from ecological and organizational research data, we show the effectiveness and predictive competitiveness of this novel estimator. The results suggest that in the presence of grouped variables, sparse-group boosting is associated with less biased variable selection and higher predictability compared to component-wise or group-component-wise boosting. [ABSTRACT FROM AUTHOR]

In the analysis of logistic regression models, various biased estimators have been proposed as an alternative to the maximum likelihood estimator (MLE) for estimating model parameters in the presence of multicollinearity. In this study, a new class of biased estimators called Logistic Ridge-type Estimator (LRTE) is proposed by generalizing the existing biased estimators that include two biasing parameters. The performance of the proposed estimator is compared with the other biased estimators in terms of the Matrix Mean Squared Error (MMSE). Two separate Monte Carlo simulation studies are conducted to investigate the performance of the proposed estimator. A numerical example is provided to demonstrate the performance of the proposed biased estimator. The results revealed that LRTE performed better than other existing biased estimators under the conditions investigated in this study. [ABSTRACT FROM AUTHOR]

GDP is a common and essential indicator for evaluating a country's overall economy. However, environmental issues may be overlooked in the pursuit of GDP growth for some countries. It may be beneficial to adopt more sustainable criteria for assessing economic health. In this study, green GDP (GGDP) is discussed using mathematical approaches. Multiple dataset indicators were selected for the evaluation of GGDP and its impact on climate mitigation. The k-means clustering algorithm was utilized to classify 16 countries into three distinct categories for specific analysis. The potential impact of transitioning to GGDP was investigated through changes in a quantitative parameter, the climate impact factor. Ridge regression was applied to predict the impact of switching to GGDP for the three country categories. The consequences of transitioning to GGDP on the quantified improvement of climate indicators were graphically demonstrated over time on a global scale. The entropy weight method (EWM) and TOPSIS were used to obtain the value. Countries in category 2, as divided by k-means clustering, were predicted to show a greater improvement in scores as one of the world's largest carbon emitters, China, which belongs to category 2 countries, plays a significant role in global climate governance. A specific analysis of China was performed after obtaining the EWM-TOPSIS results. Gray relational analysis and Pearson correlation were carried out to analyze the relationships between specific indicators, followed by a prediction of CO2 emissions based on the analyzed critical indicators. [ABSTRACT FROM AUTHOR]

According to existing literature, the ordinary least squares (OLS) estimators are not the best in presence of multicollinearity. The inability of OLS estimators against multicollinearity has paved the way for the development of various ridge type estimators for circumventing the problem of multicollinearity. In this paper improved two-parameter ridge (ITPR) estimators are proposed. A simulation study is used to evaluate the performance of proposed estimators based on minimum mean squared error (MSE) criterion. The simulative results reveal that, based on minimum MSE, ITPR2 was the most efficient estimator compared to the considered estimators in the study. Finally, a real-life dataset is analyzed to demonstrate the applications of the proposed estimators and also checked their efficacy for mitigation of multicollinearity. [ABSTRACT FROM AUTHOR]

In ridge regression, we are often concerned with acquiring ridge estimators that lead to the smallest mean square error (MSE). In this article, we have considered the problem of ridge estimation in the presence of multicollinearity and heteroscedasticity. We have introduced a scaling factor which leads to significantly improved performance of the ridge estimators as compared to their classical counterparts. For illustration purposes, we have applied our proposed methodology to some of the popular existing ridge estimators but it can be extended to other estimators as well. We have also compared our proposed estimator with popular existing estimators dealing estimation problem in the same scenario. Extensive simulations reveal the suitability of the proposed strategy, particularly in the presence of severe multicollinearity and heteroscedasticity. A real-life application highlights that the proposed strategy has the potential to be a useful tool for data analysis in the case of collinear predictors and heteroscedastic errors. [ABSTRACT FROM AUTHOR]

Instead of picking up a single ridge parameter in ridge regression, this paper considers a frequentist model averaging approach to appropriately combine the set of ridge estimators with different ridge parameters, when the response is randomly right censored. Within this context, we propose a weighted least squares ridge estimation for unknown regression parameter. A new Mallows-type weight choice criterion is then developed to allocate model weights, where the unknown distribution function of the censoring random variable is replaced by the Kaplan–Meier estimator and the covariance matrix of random errors is substituted by its averaging estimator. Under some mild conditions, we show that when the fitting model is misspecified, the resulting model averaging estimator achieves optimality in terms of minimizing the loss function. Whereas, when the fitting model is correctly specified, the model averaging estimator of the regression parameter is root-n consistent. Additionally, for the weight vector which is obtained by minimizing the new criterion, we establish its rate of convergence to the infeasible optimal weight vector. Simulation results show that our method is better than some existing methods. A real dataset is analyzed for illustration as well. [ABSTRACT FROM AUTHOR]

AbstractThis 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. [ABSTRACT FROM AUTHOR]

(1) Soil alkalinization and salinization represent a growing global challenge. Maize (Zea mays L.), with its relatively low tolerance to salt and alkali, is increasingly vulnerable to saline‐alkali stress. Identifying maize genotypes that can withstand salinity and alkalinity is crucial to broaden the base of salt‐alkali‐tolerant maize germplasm. (2) In this study, we screened 65 maize germplasm resources for alkali stress using a 60 mM NaHCO3 solution. We measured fifteen morphological and physiological indices, including seedling height, stem thickness, and leaf area. Various analytical methods—correlation analysis, principal component analysis, subordinate function analysis, cluster analysis, stepwise discriminant analysis, and ridge regression analysis—were used to assess the seedling alkali tolerance of these maize germplasm resources. The physiological indices of six tested maize varieties were analyzed in greater detail. (3) The findings revealed complex correlations among traits, particularly strong negative associations between conductivity and root traits such as length, volume, surface area, diameter, and number of branches. The 15 evaluation indices were reduced to 7 principal components, explaining 77.89% of the variance. By applying affiliation functions and weights, we derived a comprehensive evaluation of maize seedling alkali tolerance. Notably, three germplasms—Liang Yu 99, Bi Xiang 638, and Gan Xin 2818—demonstrated significant comprehensive seedling alkali tolerance. Cluster analysis grouped the 65 maize germplasm resources into four distinct categories (I, II, III, and IV). The results of the cluster analysis were confirmed by multiclass stepwise discriminant analysis, which achieved a correct classification rate of 92.3% for 60 maize genotypes regarding alkalinity tolerance. Using principal component and ridge regression analyses, we formulated a regression equation for alkali tolerance: D‐value = −1.369 + 0.002 * relative root volume + 0.003 * relative number of root forks + 0.006 * relative chlorophyll SPAD + 0.005 * relative stem thickness + 0.005 * relative plant height + 0.001 * relative conductivity + 0.002 * relative dry weight of underground parts. Under sodium bicarbonate stress, morphological indices and germination rates were significantly reduced, germination was inhibited, photosynthetic pigment levels in maize leaves decreased to varying degrees, and the activities of peroxidase (POD), superoxide dismutase (SOD), and catalase (CAT) significantly increased. Alkali stress markedly enhanced the antioxidant enzyme activities in maize varieties, with alkali‐resistant varieties exhibiting a greater increase in antioxidant enzyme activities than alkali‐sensitive varieties under such stress. (4) By screening for alkali tolerance in maize seedlings, the identified alkali‐tolerant genotypes can be further utilized as suitable donor parents, thereby enhancing the use of alkali‐tolerant germplasm resources and providing theoretical guidance for maize cultivation in saline‐alkaline environments. [ABSTRACT FROM AUTHOR]

Urban plantation dynamics in different topographical and climatic conditions in Odisha were evaluated using linear model selection and regularisation techniques. The main objective was to evaluate how and to what extent the urban plantations respond to various climatic and edaphic conditions. The relationship between vegetation growth and climatic and soil parameters was studied using four statistical learning tools, subset selection, ridge regression, lasso, and partial least squares regression, and their performance was compared to a multiple regression model. The test MSE for the subset selection, ridge regression, lasso, and partial least squares regression models was evaluated to be 16,261.54, 12245.11, 16263.79 and 14,317.21, respectively. Results proved that statistical learning methods, namely subset selection, lasso, ridge regressions and partial least squares regression, were more accurate than multiple linear regression. From the results, it can be safely concluded that temperature shows greater correlation with the growth parameters. Precipitation also plays a vital role in vegetation dynamics. Soil parameters indicate a positive correlation with that of the growth. [ABSTRACT FROM AUTHOR]

We employ an extended Stochastic Impacts by Regression on Population, Affluence and Technology (STIRPAT) model combined with the environmental Kuznets curve and machine learning algorithms, including ridge and lasso regression, to investigate the impact of institutions on carbon emissions in a sample of 22 European Union countries over 2002 to 2020. Splitting the sample into two: those with weak and strong institutions, we find that the results differ between the two groups. Our results suggest that changes in institutional quality have a limited impact on carbon emissions. Government effectiveness leads to an increase in emissions in the European Union countries with stronger institutions, whereas voice and accountability lead to a fall in emissions. In the group with weaker institutions, political stability and the control of corruption reduce carbon emissions. Our findings indicate that variables such as population density, urbanization and energy consumption are more important determinants of carbon emissions in the European Union compared to institutional governance. The results suggest the need for coordinated and consistent policies that are aligned with climate targets for the European Union as a whole. [ABSTRACT FROM AUTHOR]

Firms benefit from being reliable and trustworthy towards their customers. In many countries, however, corruption spills over to supply chain relationship practices and weakens a firm's credibility towards its customers (CTC). In this study, we investigate the influence of corruption on the relationship between CTC and firm performance. Empirical analyses of manufacturing firms in multiple countries demonstrate that corruption diminishes the effect of CTC on firms' operational performance. Moreover, a country's information and communication technology (ICT) readiness can counteract the negative impact of corruption. Our study adds to the literature on supply chain relationship management by considering the influence of two institutional contingencies (i.e. corruption and ICT readiness) on the effectiveness of CTC as an important mechanism of supply chain governance. Our study complements the literature on transaction cost economics and urges managers to consider the two characteristics of their firms' institutional environments when managing relationships in their supply chains. [ABSTRACT FROM AUTHOR]

This work is concerned with the properties of the ridge regression where the number of predictors p is proportional to the sample size n. Asymptotic properties of the means square error (MSE) of the estimated mean vector using ridge regression is investigated when the design matrix X may be non-random or random. Approximate asymptotic expression of the MSE is derived under fairly general conditions on the decay rate of the eigenvalues of X T X when the design matrix is nonrandom. The value of the optimal MSE provides conditions under which the ridge regression is a suitable method for estimating the mean vector. In the random design case, similar results are obtained when the eigenvalues of E [ X T X ] satisfy a similar decay condition as in the non-random case. [ABSTRACT FROM AUTHOR]