modehunt (version 1.0.7)

cvModeAll: Critical values for test statistic based on all intervals

Description

This dataset contains critical values for some \(n\) and \(\alpha\) for the test statistic based on all intervals, with or without additive correction term \(\Gamma\).

Usage

data(cvModeAll)

Format

A data frame providing 15 different combinations of \(n\) and \(\alpha\) 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 \(\mathcal{I}_{all}\).

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 \(f\).

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

$${\bf{U}} = (U_1,\dots,U_n)$$

where \(U_i\) is a uniformly on \([0,1]\) distributed random variable, \(i=1,\dots,M\).

References

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

Examples

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