相关论文: Generalized Ridge Regression: Applications to Nono…
When the regressors of a econometric linear model are nonorthogonal, it is well known that their estimation by ordinary least squares can present various problems that discourage the use of this model. The ridge regression is the most…
Multicollinearity produces an inflation in the variance of the Ordinary Least Squares estimators due to the correlation between two or more independent variables (including the constant term). A widely applied solution is to estimate with…
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,…
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…
General ridge estimators are widely used in the general linear model because they possess desirable properties such as linear sufficiency and linear admissibility. However, when the covariance matrix of the error term is partially unknown,…
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…
In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…
This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the…
The problem known as multicolinearity has long been recognized to fundamentally and negatively influence multiple regression. This paper does not intend to either propose a numerical assessment of the degree to which this problem exists…
The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a…
Ridge regression is a popular method for dense least squares regularization. In this work, ridge regression is studied in the context of VAR model estimation and inference. The implications of anisotropic penalization are discussed and a…
The generalized Ridge penalty is a powerful tool for dealing with overfitting and for high-dimensional regressions. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given…
In high dimensional regression, where the number of covariates is of the order of the number of observations, ridge penalization is often used as a remedy against overfitting. Unfortunately, for correlated covariates such regularisation…
Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
We propose new model selection criteria based on generalized ridge estimators dominating the maximum likelihood estimator under the squared risk and the Kullback-Leibler risk in multivariate linear regression. Our model selection criteria…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
Rank regression offers robustness to outliers and heavy-tailed response distributions, invariance to monotonic transformations, and improved efficiency under non-Gaussian errors, making it a versatile tool for analyzing complex data. This…
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…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…