cvModeAll {modehunt} | R Documentation |
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} .
|
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
.
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 criticalValuesAll
. 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(cvModeAll)
cv <- cvModeAll[cvModeAll$alpha == 0.05 & cvModeAll$n == 200, 3:4]
cv