cvModeApprox: Critical values for test statistic based on the approximating...
In modehunt: Multiscale Analysis for Density Functions

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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.

1	data(cvModeApprox)

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