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

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

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.

order of the finite mixture model under the null hypothesis, default value: m0 = 1.

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.

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 2m0EM-test statisticP-valueLevel of penalty

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.

Examples

Run this code

#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)