Subsampling estimates of the Lasso distribution.

58 Numerical results
Figure 6.1: Subsampling confidence intervals for single scenarios of the models A and A’
(n= 250). Red triangles stand for the true parameters.
Hence, for each j ∈ {1, . . . , p} we define the test φ (j)
k
, corresponding to the intervals I(j)
k
(k = 1, . . . , 4) defined in the previous section.
Rates of coverage and of false rejection based on 500 replications of the scenario are given
in tables 6.1, 6.2 and 6.3 for the two sided interval I 2 (with corresponding test φ 2 ) and a
subsample size b = n 0.85 . Results for the other intervals are omitted but it was noted that
the one sided confidence interval I 1 has rates of coverage/false rejection similar to I 2 and
that I 3 and I 4 are extremely conservative.
Fluctuations from the nominal level for the interval I 2 can be attributed to the stochastic
approximation to the true subsample quantile and to the fact that the penalization parameter
is chosen by cross-validation for each scenario. Thus the coverage/false positive
rates can be considered correct.
6.1.3 F.W.E.R
Instead of testing for individual hypotheses, one can also be interrested in testing for a
whole family of null hypotheses. The goal is then to control the probability to make