Ridge Regression: Applications to Nonorthogonal Problems

By A. E. Hoerl, R. Kennard. 1970

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Citations in the corpus

Estimation Considerations in Contextual Bandits (2017, methodology): “The model parameters can be estimated via L1 (LASSO [62] in linear models) or L2 (ridge [33] in linear models) regularized regression.”
Data-Driven Optimal Transport Cost Selection For Distributionally Robust Optimization (2017, methodology): “In which case we obtain, in the setting of (12), min The adaptive regularization method was ﬁrst derived as a generalization for ridge regression in Hoerl and Kennard (1970b) and Hoerl and Kennard (1970a).”
A review of statistical methods for the evaluation of aquatic habitat suitability for instream flow assessment (2006, methodology): “Hoerl and Kennard (1970) proposed ridge regression, a biased estimation method, which provides more stable estimates of the regression coefficients.”
Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models (2011, background): “Hoerl and Kennard (1970) showed that there exists a value of η such that that is, the mean squared error (equal to the sum of the variance and the squared bias) of the Tikhonov-regularization estimator, b(η) , is smaller than that of the OLS estimator, b .”
Some Modifications for Choosing Ridge Parameters (2006, methodology): “The generalized ridge regression estimator suggested by Hoerl and Kennard (1970a) can be written as: ̃i = ( ti ti + K̂ ) ̂i (4) where ̂ = T−1p X′Y .”
Variable Selection in Predictive Regressions (2013, methodology): “The ridge estimator (also known as Tikhonov regularization) due to Hoerl and Kennard (1970) is a special case with η = 2.”
Collinearity: a review of methods to deal with it and a simulation study evaluating their performance (2013, methodology): “An alternative that allows simultaneous optimisation of L1- and L2-norm, called the elastic net (Zou and Hastie 2005), was slightly inferior to both methods, and much slower (data not shown), though we note that newer and reputedly faster versions 780 have since been released (Friedman, et al. 2010)”
Prospects for genomic selection in conifer breeding: a simulation study of Cryptomeria japonica (2011, methodology): “To estimate the genetic effect coefficients, we used ridge regression (Hoerl and Kennard 1970).”