A Statistical View of Some Chemometrics Regression Tools

By L. Frank, Jerome H. Friedman. 1993

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Citations in the corpus

Best Subset Selection via a Modern Optimization Lens (2015, methodology): “To address the shortcomings, non-convex penalized regression is often used to “bridge” the gap between the convex `1 penalty and the combinatorial `0 penalty [38, 27, 24, 54, 55, 28, 61, 62, 57, 13].”
Component selection and smoothing in smoothing spline analysis of variance models -- COSSO (2003, methodology): “Several new and effective methods for variable selection in linear models have been proposed in recent years [Breiman (1995); Tibshirani (1996); Frank and Friedman (1993); Fan and Li (2001)].”
Envelopes and partial least squares regression (2013, background): “Frank and Friedman (1993) gave an informative discussion of PLS from various statistical views.”
Variable Selection in Predictive Regressions (2013, unknown): “While PLS is designed to shrink away from the predictor space in the low variance directions, Frank and Friedman (1993) find that PLS routinely inflates the high variance directions.”
Input-dependent estimation of generalization error under covariate shift (2005, background): “, learning with non-quadratic loss functions [16, 53, 49] or non-quadratic regularizers [10, 52, 48, 6].”
Program evaluation with high-dimensional data (2013, methodology): “This efficient influence function was derived by Hahn (1998); it was also used by Cattaneo (2010) in the series context (with p n) and Rothe and Firpo (2013) in the kernel context.”
Bridge regression: Adaptivity and group selection (2011, methodology): “1 Background Bridge regression is a broad class of the penalized regression method proposed by Frank and Friedman (1993). The bridge estimate can be obtained by minimizing”
Asymptotic properties of bridge estimators in sparse high-dimensional regression models (2008, background): “For any given γ > 0, the value β̂n that minimizes (1) is called a bridge estimator [Frank and Friedman (1993) and Fu (1998)].”
Big Data and Data Science Methods for Management Research (2016, methodology): “We refer to Frank and Friedman (1993) for a comparison of partial least squares and principal components regression.”
High-Dimensional Methods and Inference on Structural and Treatment Effects (2013, methodology): “Usual choices of r are r = 2 which corresponds to the well-known ridge regression and r = 1 which corresponds to the LASSO estimator introduced by Tibshirani (1996) and Frank and Friedman (1993). When r > 1, the solution obtained by solving (1.4) has coefficients shrunk towards zero but does not set”
A New Dimension Reduction Approach for Data-Rich Marketing Environments: Sliced Inverse Regression (2000, methodology): “In addition, Frank and Friedman (1993) found that VSS performs worse than PLSR or PCR.”
Least angle and ℓ1 penalized regression: A review (2008, background): “A bridge regression (Frank and Friedman, 1993) ℓq norm penalty with 1 q 2 is strictly convex and has a grouping effect, but does not produce a sparse solution (Fan and Li, 2001).”