forwardStop: ForwardStop rule for sequential p-values

In selectiveInference: Tools for Post-Selection Inference

Description

Computes the ForwardStop sequential stopping rule of G'Sell et al (2014)

Usage

forwardStop(pv, alpha=0.1)

Arguments

pv	Vector of **sequential** p-values, for example from fsInf or larInf
alpha	Desired type FDR level (between 0 and 1)

Details

Computes the ForwardStop sequential stopping rule of G'Sell et al (2014). Guarantees FDR control at the level alpha, for independent p-values.

Value

Step number for sequential stop.

Author(s)

Ryan Tibshirani, Rob Tibshirani, Jonathan Taylor, Joshua Loftus, Stephen Reid

References

Max Grazier G'Sell, Stefan Wager, Alexandra Chouldechova, and Rob Tibshirani (2014). Sequential selection procedures and Fflse Discovery Rate Control. arXiv:1309.5352. To appear in Journal of the Royal Statistical Society: Series B.

Examples

set.seed(33)
n = 50
p = 10
sigma = 1
x = matrix(rnorm(n*p),n,p)
beta = c(3,2,rep(0,p-2))
y = x%*%beta + sigma*rnorm(n)

# run forward stepwise
fsfit = fs(x,y)

# compute sequential p-values and confidence intervals
# (sigma estimated from full model)
out = fsInf(fsfit)
out

# estimate optimal stopping point
forwardStop(out$pv, alpha=.10)

Example output

Loading required package: glmnet
Loading required package: Matrix
Loading required package: foreach
Loaded glmnet 2.0-16

Loading required package: intervals

Attaching package: 'intervals'

The following object is masked from 'package:Matrix':

    expand

Loading required package: survival

Call:
fsInf(obj = fsfit)

Standard deviation of noise (specified or estimated) sigma = 1.027

Sequential testing results with alpha = 0.100
 Step Var   Coef Z-score P-value LowConfPt UpConfPt LowTailArea UpTailArea
    1   1  2.317  13.406   0.000     2.019    2.605       0.049      0.048
    2   2  1.703  12.996   0.000     1.486    1.922       0.048      0.050
    3   9 -0.265  -1.683   0.487    -0.782    1.152       0.050      0.050
    4   8 -0.175  -1.156   0.260    -4.764    1.532       0.050      0.050
    5  10  0.173   1.075   0.755   -12.195    3.056       0.050      0.050
    6   4 -0.178  -1.140   0.407   -11.057    7.428       0.050      0.050
    7   7  0.158   0.979   0.763    -9.225    2.137       0.050      0.050
    8   5  0.128   0.896   0.838    -6.737    0.737       0.050      0.050
    9   6 -0.036  -0.225   0.303      -Inf      Inf       0.000      0.000
   10   3  0.037   0.255   0.121    -1.478      Inf       0.050      0.000

Estimated stopping point from ForwardStop rule = 2
[1] 2

selectiveInference documentation built on Sept. 7, 2019, 9:02 a.m.