cvModeApprox {modehunt}R Documentation

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

Description

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

Usage

data(cvModeApprox)

Format

A data frame providing 15 different combinations of nn and α\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 Tn+(U)T_n^+({\bf{U}}) and the approximating set of intervals Iapp\mathcal{I}_{app}.
noadd Critical values based on Tn(U)T_n({\bf{U}}) and the approximating set of intervals Iapp\mathcal{I}_{app}.

Details

For details see modeHunting. Critical values are based on M=100000M=100'000 simulations of i.i.d. random vectors

U=(U1,,Un){\bf{U}} = (U_1,\dots,U_n)

where UiU_i is a uniformly on [0,1][0,1] distributed random variable, i=1,,Mi=1,\dots,M.

Remember

nn is the number of interior observations, i.e. if you are analyzing a sample of size mm, then you need critical values corresponding to

n = m-2 If no additional information on aa and bb is available.
n = m-1 If either aa or bb is known to be a certain finite number.
n = m If both aa and bb are known to be certain finite numbers,

where [a,b]={x : f(x)>0}[a,b] = \{x \ : \ f(x) > 0\} is the support of ff.

Source

These critical values were generated using the function criticalValuesApprox. Critical values for other combinations for α\alpha and nn 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

[Package modehunt version 1.0.7 Index]