criticalValuesApprox: Compute critical values for (1) the original test statistic...
In modehunt: Multiscale Analysis for Density Functions

Description Usage Arguments Details Value Note Author(s) References See Also Examples

This function computes critical values that can be used to perform the multiscale analysis about a density with the functions modeHuntingApprox and modeHuntingBlock.

1 2	criticalValuesApprox(n, d0 = 2, m0 = 10, fm = 2, alpha = 0.05, gam = 2, tail = 10, M = 10 ^ 5, display = 0, path = NA)

`n`	Number of observations.
`d0`	Initial parameter for the grid resolution.
`m0`	Initial parameter for the number of observations in one block.
`fm`	Factor by which m is increased from block to block.
`alpha`	Significance level, real number in (0,1).
`gam`	Weighting exponent for level in each block.
`tail`	Offset, determines together with `gam` the decrease of the level from one block to another.
`M`	Number of runs to perform.
`display`	If `display == 1`, every 100–th step is indicated in the output window, else not.
`path`	If `path != NA`, the current number of performed simulations is saved in this location.

For details see the function modeHuntingApprox and the data set cvModeApprox.

`approx`	A 2-dimensional vector containing the critical value for the test statistic with or without additive correction Γ.
`block`	A vector containing the critical value for each block.

The asymptotic results in Rufibach and Walther (2010) are only derived for f_m = 2.

Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

Guenther Walther, gwalther@stanford.edu,
www-stat.stanford.edu/~gwalther

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

The resulting critical values are used by the functions modeHuntingApprox and
modeHuntingBlock. Critical values for some combinations of n and α are available in cvModeApprox and cvModeBlock.

## compute critical values and compare to those in cvModeAll and cvModeBlock
## (to see output in R, press CTRL + W)
cv <- criticalValuesApprox(n = 200, d0 = 2, m0 = 10, fm = 2, 
     alpha = 0.05, gam = 2, tail = 10, M = 10 ^ 2, display = 1, path = NA)
cv1 <- cv$approx; cv2 <- cv$block

data(cvModeApprox); data(cvModeBlock)
cv3 <- cvModeApprox[cvModeApprox$alpha == 0.05 & cvModeApprox$n == 200, 3:4]
cv4 <- cvModeBlock[cvModeBlock$alpha == 0.05 & cvModeBlock$n == 200, 3:6]
rbind(cv1, cv3)
rbind(cv2, cv4)