Critical values for test statistic based on all intervals
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
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 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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