emtest.norm0: test the order of a mixture of normals with equal and known...

In MixtureInf: Inference for Finite Mixture Models

Description

EM-test for the order of a finite mixture of normals with equal and known variance.

Usage

emtest.norm0(x, var, m0 = 1, C = NULL, 
	     inival = NULL, len = 10, niter = 50, tol = 1e-6, k = 3, rformat = FALSE)

Arguments

x	data, can be either a vector or a matrix with the 1st column being the observed values and the 2nd column being the corresponding frequencies.
var	known component variance.
m0	order of the finite mixture model under the null hypothesis, default value: m0 = 1.
C	optional tuning parameter for EM-test procedure, default value: C = NULL. (if not provided, it will be determined by the formulas described in Chen and Li, 2011).
inival	initial values for the EM-algorithm to compute the MLE under the null model, a 2m0-dimension vector including m0 mixing proportions and m0 component parameters, or a matrix with 2m0 columns, default value: inival = NULL. (if not provided, random initial values are used.)
len	number of random initial values for the EM-algorithm, default value: len = 10.
niter	number of iterations for all initial values in the EM-algorithm. The algorithm runs EM-iteration niter times from each initial value. The iteration will restart from the parameter value with the highest likelihood value at the point and run until convergence. default value: niter = 50.
tol	tolerance level for the convergence of the EM-algorithm, default value: tol = 1e-6.
k	number of EM iterations: default value: k = 3.
rformat	form of the digital output: default of R package is used when rformat = T; If rformat = T, the digital output is rounded to the 3rd dicimal place if it is larger than 0.001, keeps 3 significant digits otherwise. The default value of rformat is F.

Value

Return an object of class EM-test with the following elements:

MLE of the parameters under the null hypothesis (order = m0)

Parameter estimates under the specific alternative whose order is 2m0

EM-test statistic

P-value

Level of penalty

Author(s)

Shaoting Li, Jiahua Chen and Pengfei Li

References

Chen, J. and Li, P. (2011). Tuning the EM-test for the order of finite mixture models. The Canadian Journal of Statistics. 39, 389–404.

Li, P. and Chen, J. (2010). Testing the order of a finite mixture model. JASA. 105, 1084–1092.

Li, P., Chen, J. and Marriott, P. (2009). Non-finite Fisher information and homogeneity: The EM approach. Biometrika. 96, 411–426.

See Also

plotmix.norm0, pmle.norm0, rmix.norm

Examples

#generate a random sample from a 2 component noraml mixture with equal variance, 
#conduct homogeneity test by the EM-test.
x <- rmix.norm(200,c(0.3,0.7),c(-1,2),c(2,2))
emtest.norm0(x,var=4)

Example output

$`MLE of parameters under null hypothesis (order = m0)`
       [,1]
alpha 1.000
theta 0.999

$`Parameter estimates under the order = 2m0`
        [,1]  [,2]
alpha  0.305 0.695
theta -0.724 1.749

$`EM-test Statistic`
[1] 7.496

$`P-value`
[1] 0.003

$`Level of penalty`
[1] 0.54

MixtureInf documentation built on May 2, 2019, 3:32 p.m.