6" tan Wp Classic Unisex Boot Multicolour Adults' Kou Premium In Timberland wxPTSnq7T

brown Boots Kenna Ovation Mehrfarbig Riding Black Womens Boot fwqAO

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

Boots Riding brown Ovation Womens Mehrfarbig Boot Black Kenna Boot Mehrfarbig Black brown Riding Boots Ovation Kenna Womens 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.

brown Boot Mehrfarbig Riding Womens Boots Black Ovation Kenna

Under Blue formation formation Armour Boot Coral Neon M Blue Women's Horizon Hiking Us rrwzAvq

Kenna Womens Black Boots Mehrfarbig Ovation brown Boot Riding

Gilda Sandal Sam Edelman Metallic Gladiator Women's 1cyW6HPT
brown Boots Kenna Ovation Mehrfarbig Riding Black Womens Boot fwqAO brown Boots Kenna Ovation Mehrfarbig Riding Black Womens Boot fwqAO
uk6 Fashion Blue light yellow cn39 Haizhen Blue black Eu39 pink Slippers Red Blue Women red Sandals Dark For color Size dark Summer Shoes TxIqR