test the order of a mixture of normals with unequal variance

Description

EM-test for the order of a finite mixture of normals with unequal variance.

Usage

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emtest.norm(x, m0 = 1, pens = 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 the observed values and the 2nd column being the corresponding frequencies.

m0

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

pens

a 2-dimensions vector with the level of penalty functions for mixing proportion and variance, default value: pens = NULL. (if not provided, it will be determined by the formulas described in Chen, Li and Fu, 2012)

inival

initial values for the EM-algorithm to compute the MLE under the null model, a 3m0-dimensions vector including m0 mixing proportions, m0 component means and m0 component variances, or a matrix with 3m0 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. (2009). Hypothesis test for normal mixture models: The EM approach. The Annals of Statistics. 37, 2523–2542.

Chen, J., Li, P. and Fu, Y. (2012). Inference on the order of a normal mixture. JASA. 107, 1096–1105.

See Also

plotmix.norm, pmle.norm, rmix.norm

Examples

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#load the grains data set,
#conduct homogeneity test by the EM-test.
data(grains)
emtest.norm(grains)

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