The estimation of ridge parameter is an important problem in the ridge regression method, which is widely used to solve multicollinearity problem. A comprehensive study on 28 different available estimators and five proposed ridge estimators, KB1, KB2, KB3, KB4, and KB5, is provided. A simulation study was conducted and selected estimators were compared. Some of selected ridge estimators perform...

This paper introduces an information theoretic model selection and ridge parameter estimation criterion for generalized linear models based on the minimum message length principle. The criterion is highly general in nature, and handles a range of target distributions, including the normal, binomial, Poisson, geometric and gamma distributions. Estimation of the regression parameters, the ridge h...

Anomalies persist in the foundations of ridge regression as set forth in Hoerl and Kennard (1970) and subsequently. Conventional ridge estimators and their properties do not follow on constraining lengths of solution vectors using LaGrange’s method, as claimed. Estimators so constrained have singular distributions; the proposed solutions are not necessarily minimizing; and heretofore undiscover...

When independent variables have high linear correlation in a multiple linear regression model, we can have wrong analysis. It happens if we do the multiple linear regression analysis based on common Ordinary Least Squares (OLS) method. In this situation, we are suggested to use ridge regression estimator. We conduct some simulation study to compare the performance of ridge regression estimator ...

In ridge regression the estimation of the ridge parameter is an important issue. This paper generalizes some methods for estimating the ridge parameter for probit ridge regression (PRR) model based on the work of Kibria et al. (2011). The performance of these new estimators are judged by calculating the mean square error (MSE) using Monte Carlo simulations. In the design of the experiment we ch...

In estimation of the large precision matrix, this paper suggests a new shrinkage estimator, called the linear ridge estimator. This estimator is motivated from a Bayesian aspect for a spike and slab prior distribution of the precision matrix, and has a form of convex combination of the ridge estimator and the identity matrix multiplied by scalar. The optimal parameters in the linear ridge estim...

The average ridge distance of fingerprint images is a very important parameter for fingerprint image enhancement, which will greatly affect the performance of fingerprint recognition. A method of efficient ridge distance estimation based on typical image blocks is proposed. First, we obtain some typical candidate image blocks through the initial selection according to the orientation curvature ...

Ridge regression, being based on the minimization of a quadratic loss function, is sensitive to outliers. Current proposals for robust ridge regression estimators are sensitive to “bad leverage observations”, cannot be employed when the number of predictors p is larger than the number of observations n; and have a low robustness when the ratio p=n is large. In this paper a ridge regression esti...

The paper presents the combined ridge-stein estimator (CRS) for linear pushbroom imagery exterior orientation, which is severely ill-conditioned for the strong correlation among exterior orientation elements of linear pushbroom imagery. The estimator is a new biased method combining the ridge estimator and the stein estimator. It can effectively change the ill-conditioned state of linear pushbr...