Abstract: Identifying influential observations is an important part of the model building process in linear regression. There are numerous diagnostic measures based on different approaches in linear regression analysis. However, the problem of multicollinearity and influential observations may occur simultaneously. Therefore, we propose new diagnostic measures based on the two parameter ridge e...

Ridge regression is one of the most popular and effective regularized regression methods, and one case of particular interest is that the number of features p is much larger than the number of samples n, i.e. p n. In this case, the standard optimization algorithm for ridge regression computes the optimal solution x⇤ in O(n2p + n3) time. In this paper, we propose a fast relativeerror approximati...

Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing MSE (mean square error) has been recognized in multiple regression analysis for some time, especially when predictor variables are nearly collin...

In recent years, there has been a considerable amount of research on the use of regularization methods for inference and prediction in quantitative genetics. Such research mostly focuses on selection of markers and shrinkage of their effects. In this review paper, the use of ridge regression for prediction in quantitative genetics using single-nucleotide polymorphism data is discussed. In parti...

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...

BACKGROUND Genomic selection (GS) is emerging as an efficient and cost-effective method for estimating breeding values using molecular markers distributed over the entire genome. In essence, it involves estimating the simultaneous effects of all genes or chromosomal segments and combining the estimates to predict the total genomic breeding value (GEBV). Accurate prediction of GEBVs is a central...

We propose a fast algorithm for ridge regression when the number of features is much larger than the number of observations (p n). The standard way to solve ridge regression in this setting works in the dual space and gives a running time of O(np). Our algorithm Subsampled Randomized Hadamard TransformDual Ridge Regression (SRHT-DRR) runs in time O(np log(n)) and works by preconditioning the de...

Adaptive ridge is a special form of ridge regression, balancing the quadratic penalization on each parameter of the model. This paper shows the equivalence between adaptive ridge and lasso (least absolute shrinkage and selection operator). This equivalence states that both procedures produce the same estimate. Least absolute shrinkage can thus be viewed as a particular quadratic penalization. F...