相关论文: Ridge TRACE Diagnostics

A new generalized ridge regression shrinkage path is proposed that is as short as possible under the restriction that it must pass through the vector of regression coefficient estimators that make the overall Optimal Variance-Bias Trade-Off…

In this study, we propose shrinkage methods based on {\it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also,…

Beta regression model is useful in the analysis of bounded continuous outcomes such as proportions. It is well known that for any regression model, the presence of multicollinearity leads to poor performance of the maximum likelihood…

We consider the application of a popular penalised regression method, Ridge Regression, to data with very high dimensions and many more covariates than observations. Our motivation is the problem of out-of-sample prediction and the setting…

Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this…

A Two-Stage approach enables researchers to make optimal non-linear predictions via Generalized Ridge Regression using models that contain two or more x-predictor variables and make only realistic minimal assumptions. The optimal regression…

While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…

In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were…

This paper analyzes the possibilities of using the generalized ridge regression to mitigate multicollinearity in a multiple linear regression model. For this purpose, we obtain the expressions for the estimated variance, the coefficient of…

Regularized regression techniques for linear regression have been created the last few ten years to reduce the flaws of ordinary least squares regression with regard to prediction accuracy. In this paper, new methods for using regularized…

The large amount of online data and vast array of computing resources enable current researchers in both industry and academia to employ the power of deep learning with neural networks. While deep models trained with massive amounts of data…

Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=\Sigma^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $\Sigma$ is shared by all…

We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do…

High-dimensional biomarkers such as genomics are increasingly being measured in randomized clinical trials. Consequently, there is a growing interest in developing methods that improve the power to detect biomarker-treatment interactions.…

Ranked set sampling (RSS) is used as a powerful data collection technique for situations where measuring the study variable requires a costly and/or tedious process while the sampling units can be ranked easily (e.g., osteoporosis…

Ridge regression is a well established regression estimator which can conveniently be adapted for classification problems. One compelling reason is probably the fact that ridge regression emits a closed-form solution thereby facilitating…

From benign overfitting in overparameterized models to rich power-law scalings in performance, simple ridge regression displays surprising behaviors sometimes thought to be limited to deep neural networks. This balance of phenomenological…

A Two-Stage approach is described that literally "straighten outs" any potentially nonlinear relationship between a y-outcome variable and each of p = 2 or more potential x-predictor variables. The y-outcome is then predicted from all p of…

We derive the ideal train/test split for the ridge regression to high accuracy in the limit that the number of training rows m becomes large. The split must depend on the ridge tuning parameter, alpha, but we find that the dependence is…

This paper studies transfer learning for ridge-regularized robust linear regression in the moderate-dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed…