[A Statistical View of Some Chemometrics Regression Tools]: Discussion

By Trevor J. Hastie, Colin L. Mallows. 1993

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High-dimensional graphs and variable selection with the Lasso (2006, background): “Other regression estimates have been proposed, which are based on the /p-norm, where p is typically in the range [0, 2] (see [7]).”
Penalized Q-Learning for Dynamic Treatment Regimens (2015, methodology): “Using individual selection enjoys similar shrinkage advantages as do penalized methods described by Frank and Friedman (1993), Tibshirani (1996), Fan and Li (2001), Candes and Tao (2007), Zou (2006) and Zou and Li (2008).”
THE Mnet method for variable selection (2016, methodology): “Several important methods have been proposed, which include estimators based on the `2 penalty (ridge regression, Hoerl and Kennard 1970), the bridge penalty (Frank and Friedman 1993), the `1 penalty or the least absolute shrinkage and”
Linear functional regression: The case of fixed design and functional response (2002, background): “…Boente and Fraiman (2000), Bosq (1991), Brumback and Rice (1998), Dauxois, Pousse and Romain (1982), 2 Fan and Lin (1998), Ferraty and Vieu (1999), Hastie and Mallows (1993), Kneip (1994), Kneip and Gasser (1992), Locantore et al. (1999), Ramsay and Dalzell (1991), Rice and Silverman (1991) and…”
Generalized linear models with functional predictors (2002, background): “Hastie and Mallows (1993) and Ramsay and Silverman (1997) (chapter 10) discussed performing regression where the response is a scalar and the predictors functional but they primarily addressed the situation where the predictors are all measured at the same time points.”
A general framework for functional regression modelling (2017, background): “To our knowledge, this approach was first described for the scalar-on-function case in Marx and Eilers (1999, 2005), with some early work given in Hastie and Mallows (1993).”
A unified approach to model selection and sparse recovery using regularized least squares (2009, background): “To name a few in addition to those work mentioned before, Frank and Friedman (1993) propose the bridge regression.”
The pls Package: Principal Component and Partial Least Squares Regression in R (2007, background): “In turn, both behave very similar to ridge regression (Frank and Friedman 1993).”
Sparse estimators and the oracle property, or the return of Hodges’ estimator (2007, unknown): “Examples are the class of Bridge estimators introduced by Frank and Friedman (1993), which includes Lasso-type estimators as a special case (Knight and Fu (2000)), or the smoothly clipped absolute deviation (SCAD) estimator introduced in Fan and Li (2001) and further discussed in Fan and Li (2002,…”
A Selective Overview of Variable Selection in High Dimensional Feature Space (2009, methodology): “A natural generalization of penalized L 0 -regression is penalized L q -regression, called bridge regression in Frank and Friedman (1993), in which p λ ( θ ) = λ θ q for 0 q ≤ 2.”
Prediction by Supervised Principal Components (2006, background): “PLS is one such approach, with a long history (Wold 1975; Frank and Friedman 1993; Hastie, Tibshirani, and Friedman 2001).”
Dimension reduction and coefficient estimation in multivariate linear regression (2007, background): “In recent years, considerable effort has also been devoted to the more general situations with q > 1 (Frank and Friedman, 1993; Bedrick and Tsai, 1994; Fujikoshi and Satoh, 1997; Brown et al., 1998, 1999, 2002; Turlach et al., 2005; Lutz and Bühlmann, 2006).”