Critical values for test statistic based on the approximating set of intervals
Description
This dataset contains critical values for some n and α for the test statistic based on the approximating set of intervals, with or without additive correction term Γ.
Usage
1 
Format
A data frame providing 15 different combinations of n and α and the following columns:
alpha  The levels at which critical values were simulated. 
n  The number of observations for which critical values were simulated. 
withadd  Critical values based on T_n^+({\bf{U}}) and the approximating set of intervals \mathcal{I}_{app}. 
noadd  Critical values based on T_n({\bf{U}}) and the approximating set of intervals \mathcal{I}_{app}. 
Details
For details see modeHunting
. Critical values are based on
M=100'000 simulations of i.i.d. random vectors
{\bf{U}} = (U_1,…,U_n)
where U_i is a uniformly on [0,1] distributed random variable, i=1,…,M.
Remember
n is the number of interior observations, i.e. if you are analyzing a sample of size m, then you need critical values corresponding to
n = m2  If no additional information on a and b is available. 
n = m1  If either a or b is known to be a certain finite number. 
n = m  If both a and b are known to be certain finite numbers, 
where [a,b] = \{x \ : \ f(x) > 0\} is the support of f.
Source
These critical values were generated using the function criticalValuesApprox
. Critical values
for other combinations for α and n can be computed using this latter function.
References
Rufibach, K. and Walther, G. (2010). A general criterion for multiscale inference. J. Comput. Graph. Statist., 19, 175–190.
Examples
1 2 3 4  ## extract critical values for alpha = 0.05, n = 200
data(cvModeApprox)
cv < cvModeApprox[cvModeApprox$alpha == 0.05 & cvModeApprox$n == 200, 3:4]
cv
