Description Usage Arguments Details Value See Also Examples
Function to generate a datMix
object to be passed to other mixComp
functions used for estimating the mixture complexity.
1 2 3 4 5 6 7 
dat 
a numeric vector containing the observations from the mixture model. 
dist 
a character string giving the (abbreviated) name of the component distribution, such that the function 
theta.bound.list 
a named list specifying the upper and the lower bound for the component parameters. The names of the list elements have to match the names of the formal arguments of the functions 
MLE.function 
function (or list of functions) which takes as input the data and gives as output the maximum likelihood estimator for the parameter(s) of a one component mixture (i.e. the standard MLE of the component distribution 
Hankel.method 
character string in 
Hankel.function 
function needed for the moment estimation via 
x 

... 
further arguments passed to the print method. 
If the datMix
object is supposed to be passed to a function that calculates the Hankel matrix of the moments of the mixing distribution (i.e. nonparamHankel
, paramHankel
or paramHankel.scaled
), the arguments Hankel.method
and Hankel.function
have to be specified. The Hankel.method
s that can be used to generate the estimate of the (raw) moments of the mixing distribution and the corresponding Hankel.function
s are the following, where j specifies an estimate of the number of components:
"explicit"
For this method, Hankel.function
contains a function with arguments called dat
and j
, explicitly estimating the moments of the mixing distribution from the data and the currently assumed mixture complexity. Note that what DacunhaCastelle & Gassiat (1997) called the "natural" estimator in their original paper is equivalent to using "explicit"
with Hankel.function
f_j((1/n) * sum_i(ψ_j(X_i))).
"translation"
This method corresponds to DacunhaCastelle & Gassiat's (1997) example 3.1. It is applicable if the family of component distributions (G_θ) is given by dG_θ(x) = dG(xθ), where G is a known probability distribution whose moments can be given explicitly. Hankel.function
contains a function of j returning the jth (raw) moment of G.
"scale"
This method corresponds to DacunhaCastelle & Gassiat's (1997) example 3.2. It is applicable if the family of component distributions (G_θ) is given by dG_θ(x) = dG(x\θ), where G is a known probability distribution whose moments can be given explicitly. Hankel.function
contains a function of j returning the jth (raw) moment of G.
If the datMix
object is supposed to be passed to a function that estimates the component weights and parameters (i.e. all but nonparamHankel
), the argument theta.bound.list
has to be specified, and MLE.function
will be used in the estimation process if it is supplied (otherwise the MLE is found numerically).
Note that the datMix
function will change the random number generator (RNG) state.
An object of class datMix
with the following attributes (for further explanations
see above):
dist 

discrete 
logical indicating whether the underlying mixture distribution is discrete. 
theta.bound.list 

MLE.function 

Hankel.method 

Hankel.function 
RtoDat
for the conversion of rMix
to datMix
objects.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38  ## observations from a (presumed) mixture model
obs < faithful$waiting
## generate list of parameter bounds (assuming gaussian components)
norm.bound.list < vector(mode = "list", length = 2)
names(norm.bound.list) < c("mean", "sd")
norm.bound.list$mean < c(Inf, Inf)
norm.bound.list$sd < c(0, Inf)
## generate MLE functions
# for "mean"
MLE.norm.mean < function(dat) mean(dat)
# for "sd" (the sd function uses (n1) as denominator)
MLE.norm.sd < function(dat){
sqrt((length(dat)  1) / length(dat)) * sd(dat)
}
# combining the functions to a list
MLE.norm.list < list("MLE.norm.mean" = MLE.norm.mean,
"MLE.norm.sd" = MLE.norm.sd)
## function giving the j^th raw moment of the standard normal distribution,
## needed for calculation of the Hankel matrix via the "translation" method
## (assuming gaussian components with variance 1)
mom.std.norm < function(j){
ifelse(j %% 2 == 0, prod(seq(1, j  1, by = 2)), 0)
}
## generate 'datMix' object
faithful.dM < datMix(obs, dist = "norm", theta.bound.list = norm.bound.list,
MLE.function = MLE.norm.list, Hankel.method = "translation",
Hankel.function = mom.std.norm)
## using 'datMix' object to estimate the mixture complexity
set.seed(1)
res < paramHankel.scaled(faithful.dM)
plot(res)

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