Fit SansSouciStruct object
Arguments
- object
An object of class
SansSouciStruct
- alpha
Target risk (JER) level
- p.values
A vector of length
nHyp(object)
,- family
A character value describing how the number of true nulls in a set is estimated. Can be either:
"DKWM": estimation by the Dvoretzky-Kiefer-Wolfowitz-Massart inequality (related to the Storey estimator of the proportion of true nulls), valid for independent p-values
"HB": estimation by the Holm-Bonferroni method, always valid
"trivial": dummy estimation as the the size of the set
"Simes": estimation via the Simes inequality, valid for positively-dependent (PRDS) p-values
"Oracle": true number of true null hypotheses Truth" must be available in
object$input$truth
- flavor
A character value which can be
"tree" (default value): the reference family is the entire tree structure
"partition": the reference family is the partition corresponding to the leaves of the tree
- ...
Not used
Value
A 'fitted' object of class 'SansSouciStruct'. It is a list of three elements
input: see SansSouciStruct
param: the input parameters, given as a list
output: a list of two elements
p.values: the input argument 'p.values'
ZL: the output of the "zeta function" associated to the input parameter 'family', see e.g. zeta.DKWM
Details
In the particular case where family=="Simes"
or family=="Oracle"
, the return value is actually of class SansSouci
and not SansSouciStruct
References
Durand, G., Blanchard, G., Neuvial, P., & Roquain, E. (2020). Post hoc false positive control for structured hypotheses. Scandinavian Journal of Statistics, 47(4), 1114-1148.
Dvoretzky, A., Kiefer, J., and Wolfowitz, J. (1956). Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. The Annals of Mathematical Statistics, pages 642-669.
Holm, S. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6 (1979), pp. 65-70.
Massart, P. (1990). The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality. The Annals of Probability, pages 1269-1283.
Examples
s <- 100
q <- 7
m <- s*2^q
obj <- SansSouciDyadic(m, leaf_size = s, direction = "top-down")
mu <- gen.mu.leaves(m = m, K1 = 8, d = 0.9, grouped = TRUE,
setting = "const", barmu = 3, leaf_list = obj$input$leaves)
pvalues <- gen.p.values(m = m, mu = mu, rho = 0)
alpha <- 0.05
S1 <- which(mu != 0)
res_DKWM <- fit(obj, alpha, pvalues, "DKWM")
predict(res_DKWM, S = S1, what = "FP")
#> [1] 348
res_Simes <- fit(obj, alpha, pvalues, "Simes")
predict(res_Simes, S = S1, what = "FP")
#> [1] 584