lambdaGroupSLOPE {grpSLOPE}

Regularizing sequence for Group SLOPE

Description

Generate the regularizing sequence lambda for the Group SLOPE problem according to one of multiple methods (see Details).

Usage

lambdaGroupSLOPE(method, fdr, group, wt, n.obs = NULL)

Arguments

method

Possible values are "max", "mean", and "corrected". See under Details.

fdr

Target group false discovery rate (gFDR)

group

A vector describing the grouping structure. It should contain a group id for each predictor variable.

wt

A named vector of weights, one weight per group of predictors (named according to names as in vector group)

n.obs

Number of observations (i.e., number of rows in A); required only if method is "corrected"

Details

Multiple methods are available to generate the regularizing sequence lambda:

• "max" – lambdas as in Theorem 2.5 in Brzyski et. al. (2016). Provalby controls gFDR in orthogonal designs.

• "mean" – lambdas of equation (2.16) in Brzyski et. al. (2016). Applicable for gFDR control in orthogonal designs. Less conservative than "max".

• "corrected" – lambdas of Procedure 1 in Brzyski et. al. (2016); in the special case that all group sizes are equal and wt is a constant vector, Procedure 6 of Brzyski et. al. (2016) is applied. Applicable for gFDR control when predictors from different groups are stochastically independent.

Value

A vector containing the calculated lambda values.

References

D. Brzyski, A. Gossmann, W. Su, and M. Bogdan (2016) Group SLOPE – adaptive selection of groups of predictors, https://arxiv.org/abs/1610.04960

D. Brzyski, A. Gossmann, W. Su, and M. Bogdan (2019) Group SLOPE – adaptive selection of groups of predictors. Journal of the American Statistical Association 114 (525): 419–33.

Examples

# specify 6 groups of sizes 2, 3, and 4
group <- c(1, 1, 2, 2, 2, 3, 3, 3, 3,
           4, 4, 5, 5, 5, 6, 6, 6, 6)
# set the weight for each group to the square root of the group's size
wt <- rep(c(sqrt(2), sqrt(3), sqrt(4)), 2)
names(wt) <- 1:6
# compute different lambda sequences
lambda.max <- lambdaGroupSLOPE(method="max", fdr=0.1, group=group, wt=wt) 
lambda.mean <- lambdaGroupSLOPE(method="mean", fdr=0.1, group=group, wt=wt) 
lambda.corrected <- lambdaGroupSLOPE(method="corrected", fdr=0.1,
                                     group=group, wt=wt, n.obs=1000)
rbind(lambda.max, lambda.mean, lambda.corrected)
#                      [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
# lambda.max       2.023449 1.844234 1.730818 1.645615 1.576359 1.517427
# lambda.mean      1.880540 1.723559 1.626517 1.554561 1.496603 1.447609
# lambda.corrected 1.880540 1.729811 1.637290 1.568971 1.514028 1.467551