cvModeApprox: Critical values for test statistic based on the approximating...

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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.




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}.


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.


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.


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.


Rufibach, K. and Walther, G. (2010). A general criterion for multiscale inference. J. Comput. Graph. Statist., 19, 175–190.


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

modehunt documentation built on May 19, 2017, 2:29 p.m.
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