Critical values for test statistic based on all intervals

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Description

This dataset contains critical values for some n and α for the test statistic based on all intervals, with or without additive correction term Γ.

Usage

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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 set of all intervals \mathcal{I}_{all}.
noadd Critical values based on T_n({\bf{U}}) and the set of all intervals \mathcal{I}_{all}.

Details

For details on the above test statistics 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 = m-2 If no additional information on a and b is available.
n = m-1 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 criticalValuesAll. 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

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## extract critical values for alpha = 0.05, n = 200
data(cvModeAll)
cv <- cvModeAll[cvModeAll$alpha == 0.05 & cvModeAll$n == 200, 3:4]
cv