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...

Kernel ridge regression is gaining popularity as a data-rich nonlinear forecasting tool, which is applicable in many different contexts. This paper investigates the influence of the choice of kernel and the setting of tuning parameters on forecast accuracy. We review several popular kernels, including polynomial kernels, the Gaussian kernel, and the Sinc kernel. We interpret the latter two kern...

This paper derives an identity connecting the square loss of ridge regression in on-line mode with the loss of the retrospectively best regressor. Some corollaries about the properties of the cumulative loss of on-line ridge regression are also obtained.

T HE introduction by Hoerl and Kennard (1970) of a ridge regression estimator to deal with the problem of multicollinearity in regression has been followed by a large number of papers in the statistical literature. In the area of econometrics, though, the method of ridge regression has received little attention. I One of the reasons for the lack of interest in ridge regression on the part of th...