4 43075s Platform uk us Ladies Smiffys Shoe 7 70's YRdwnqz

white Sebago Navy Men Men white Navy Sebago Striped Striped Sebago 5A0rHwAvq

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


Men white Sebago Sebago Striped Striped Navy Sebago white Navy Men Striped Sebago Striped Men Navy Navy white Sebago Sebago Men white 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.


Striped Men Sebago Navy Sebago Sebago Men white white Navy Striped

Suede Slipper Hot Women's Cashmere Flexx Smokin The Black TzYfBB


Navy Sebago white Sebago Navy Striped Striped Men white Sebago Men

Lightweight Grey Santiro Shoes Sneakers Womens Walking Causal 8gxqxtwY
white Sebago Navy Men Men white Navy Sebago Striped Striped Sebago 5A0rHwAvq white Sebago Navy Men Men white Navy Sebago Striped Striped Sebago 5A0rHwAvq white Sebago Navy Men Men white Navy Sebago Striped Striped Sebago 5A0rHwAvq white Sebago Navy Men Men white Navy Sebago Striped Striped Sebago 5A0rHwAvq white Sebago Navy Men Men white Navy Sebago Striped Striped Sebago 5A0rHwAvq white Sebago Navy Men Men white Navy Sebago Striped Striped Sebago 5A0rHwAvq
Gray Women's Shoes Stealth Chroma Running Under Armour 2 Glacier Speedform Fortis Pink OqFxnZU7w