Rank-Based Methods for Shrinkage and Selection. A. K. Md. Ehsanes Saleh
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Название: Rank-Based Methods for Shrinkage and Selection

Автор: A. K. Md. Ehsanes Saleh

Издательство: John Wiley & Sons Limited

Жанр: Математика

Серия:

isbn: 9781119625421

isbn:

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      1.1 Four plots using different versions of the telephone data set with fitted lines.

      1.2 Histograms and ordered residual plots of LS and Theil estimators.

      1.3 Effect of a single outlier on LS and rank estimators.

      1.4 Gradients of absolute value (Bn′(θ)) and dispersion (Dn′(θ)) functions.

      1.5 Scoring functions ϕ(u)=12(u−0.5) and ϕ+(u)=3u.

      1.6 Dispersion functions and derivative plots for 1.1(d).

      1.7 Key shrinkage characteristics of LASSO and ridge.

      1.8 Geometric interpretation of ridge.

      1.9 Geometric interpretation of LASSO.

      2.1 The first-order nature of shrinkage due to ridge.

      2.2 Two outliers found in the Q–Q plot for the Swiss data set.

      2.3 Sampling distributions of rank estimates.

      2.4 Shrinkage of β5 due to increase in ridge tuning parameter, λ2.

      2.5 Ridge traces for orthonormal, diagonal, LS, and rank estimators (m = 40).

      2.6 MSE Derivative plot to find optimal λ2 for the diagonal case.

      2.7 Bias, variance and MSE for the Swiss data set (optimal λ2 = 70.8).

      2.8 MSE for training, CV and test sets, and coefficients from the ridge trace.

      2.9 The first-order nature of shrinkage due to LASSO.

      2.10 Diamond-warping effect of weights in the aLASSO estimator for p = 2.

      2.11 Comparison of LASSO and aLASSO traces for the Swiss data set.

      2.12 Variable ordering from R-LASSO and R-aLASSO traces for the Swiss data set.

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