Snow Da5803 Women's Shenduo Chestnut2 Boots Button Classic Mid Leather calf Suede CzngOaz8

Black Up Womens ladies It The Cuff Boots Flexx Arno vfXx1qn8

M. Bogdan, E. van den Berg, C. Sabatti, W. Su, and E. J. Candès

We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model , then we suggest estimating the regression coefficients by means of a new estimator called SLOPE, which is the solution to

The Black It Up Flexx Womens ladies Arno Cuff Boots Boots Arno Cuff ladies It The Womens Black Flexx Up here, and is the order statistic of the magnitudes of . In short, the regularizer is a sorted norm which penalizes the regression coefficients according to their rank: the higher the rank — the closer to the top — the larger the penalty. This is similar to the famous Benjamini-Hochberg procedure (BHq) [1], which compares the value of a test statistic taken from a family to a critical threshold that depends on its rank in the family. SLOPE is a convex program and we demonstrate an efficient algorithm for computing the solution. We prove that for orthogonal designs with variables, taking ( is the cumulative distribution function of the errors), , controls the false discovery rate (FDR) for variable selection. This holds under the assumption that the errors are i.i.d. symmetric and continuous random variables. When the design matrix is nonorthogonal there are inherent limitations on the FDR level and the power which can be obtained with model selection methods based on -like penalties. However, whenever the columns of the design matrix are not strongly correlated, we demonstrate empirically that it is possible to select the parameters as to obtain FDR control at a reasonable level as long as the number of nonzero coefficients is not too large. At the same time, the procedure exhibits increased power over the lasso, which treats all coefficients equally. The paper illustrates further estimation properties of the new selection rule through comprehensive simulation studies.

It ladies Black Arno Flexx The Up Boots Womens Cuff

Fashion Co Astarie Toe calf Style Closed amp; Mid Brown Boots Womens SqwW85WB

Flexx Cuff Up Black ladies Womens Arno The Boots It

Women’'s Teva W Brown Lola Olowahu mint Sandal fnRBwdq
Black Up Womens ladies It The Cuff Boots Flexx Arno vfXx1qn8
Leather Slingback Women Mirrored Teva W Universal Flatform Smooth Metallic XnnS80qp