On Fri, 4 Nov 2011, bonda wrote:
The 2006 CSDA paper is really very informative, perhaps, I'm trying to
understand the things lying beyond. If we have e.g. k=3, then taking
nproc=3 for the functional maxBB we get a critical value (boundary)
maxBB$computeCritval(0.05,nproc=3)
[1] 1.544421,
and this for nproc=NULL (Bonferroni approximation) will be
maxBB$computeCritval(0.05)
[1] 1.358099.
No. In the latter case no Bonferroni approximation is applied. If you want
to use it, you can do so via the rule of thumb
R> maxBB$computeCritval(0.05/3, nproc = 1)
[1] 1.547175
which essentially matches the critical value computed for nproc = 3. If
you use the more precise value 1 - (1 - 0.05)^(1/3) instead of 0.05/3, you
get a match (up to some small numerical differences).
Setting nproc=NULL is only possible in efpFunctional():
efpFunctional() sets up the computeCritval() and computePval() functions
via simulation methods (unless closed form solutions are supplied). For
the simulation two strategies are available: Simulate nproc = 1, 2, 3, ...
explicitly. Simulate only nproc = 1 and apply a Bonferroni correction. The
last option is chosen if you set nproc=NULL -- it makes only sense if you
aggregate via the maximum across the components.
The resulting computeCritval() and computePval() function always need to
have the correct nproc supplied (i.e., nproc=NULL makes no sense).
Aggregating 3 Brownian bridges first over components, we obtain time series
process. Now, we wonder if maximum value of the process (aggregation over
time) lies over boundary. Which boundary - 1.544421 or 1.358099 - should one
take? They look too different and, for instance, lead to "unfair computing"
of empirical size (as rejection rate of null hypothesis) or empirical power
(as acception rate of alternative).
--
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