wle.normal.mixture is a preliminary version; it is used to robust estimate the location, scale and proportion parameters via Weighted Likelihood, when the sample is iid from a normal mixture univariate distribution with known m number of components.
the number of starting points based on boostrap subsamples to use in the search of the roots.
group
the dimension of the bootstap subsamples. The default value is max(round(size/4),2) where size is the number of observations.
num.sol
maximum number of roots to be searched.
raf
type of Residual adjustment function to be use:
raf="HD": Hellinger Distance RAF,
raf="NED": Negative Exponential Disparity RAF,
raf="SCHI2": Symmetric Chi-Squared Disparity RAF.
smooth
the value of the smoothing parameter.
tol
the absolute accuracy to be used to achieve convergence of the algorithm.
equal
the absolute value for which two roots are considered the same. (This parameter must be greater than tol).
max.iter
maximum number of iterations.
all.comp
try to find all the components.
min.size
see details
min.weights
see details
boot.start
the number of starting points for the starting process.
group.start
the dimension of the bootstap subsamples in the starting process. The default value is max(round(group/4),2).
tol.start
the absolute accuracy to be used to achieve convergence of the algorithm in the starting process.
equal.start
the absolute value for which two roots are considered the same in the starting process. (This parameter must be greater than tol.start).
smooth.start
the value of the smoothing parameter in the starting process.
max.iter.start
maximum number of iterations in the starting process.
max.iter.boot
maximum number of iterations of the starting process.
verbose
if TRUE warnings are printed.
Details
this function use an iterative procedure to evaluate starting
points. First, using wle.normal we try to find the biggest
components, then we discard each observation with weight greater than
min.weights. The wle.normal is run on the remain
observations if the ratio between the number of observations and the
original sample size is greater than min.size. The convergence of
the algorithm is determined by the difference between two
iterations. This stopping rule could have some problems, as soon as
possible it will replace with the one proposed in Markatou (2000)
pag. 485 (5).
Value
wle.normal.mixture returns an object of class"wle.normal.mixture".
Only print method is implemented for this class.
The objects returned by wle.normal.mixture are:
location
the estimator of the location parameters, one vector for each root found.
scale
the estimator of the scale parameters, one vector for each root found.
pi
the estimator of the proportion parameters, one vector for each root found.
tot.weights
the sum of the weights, divide by the number of observations, one value for each root found.
weights
the weights associated to each observation, one column vector for each root found.
f.density
the non-parametric density estimation.
m.density
the smoothed model.
delta
the Pearson residuals.
freq
the number of starting points converging to the roots.
tot.sol
the number of solutions found.
not.conv
the number of starting points that does not converge after the max.iter iteration are reached.
call
the match.call().
Author(s)
Claudio Agostinelli
References
Markatou, M., (2000) Mixture models, robustness and the weighted likelihood methodology, Biometrics, 56, 483-486.
Markatou, M., (2001) A closer look at the weighted likelihood in the context of mixtures, Probability and Statistical Models with Applications, Charalambides, C.A., Koutras, M.V. and Balakrishnan, N. (eds.), Chapman and Hall/CRC, 447-467.
Examples
library(wle)
set.seed(1234)
x <- c(rnorm(150,0,1),rnorm(50,15,2))
wle.normal.mixture(x,m=2,group=50,group.start=2,boot=5,num.sol=3)
wle.normal(x,group=2,boot=10,num.sol=3)