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

In modehunt: Multiscale Analysis for Density Functions

Critical values for test statistic based on the approximating set of intervals

Description

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

Usage

data(cvModeApprox)

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 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,\dots,U_n)

where U_i is a uniformly on [0,1] distributed random variable, i=1,\dots,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 criticalValuesApprox. Critical values for other combinations for \alpha 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

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

modehunt documentation built on June 8, 2025, 9:38 p.m.