emtest.exp: test the order of a mixture of exponentials

Description

EM-test for the order of a finite mixture of exponentials.

Usage

emtest.exp(x, 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.

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 exponential mixture,
#test for order = 2 by the EM-test,
#plot the histogram of the observations and the fitted density under the null model.
x <- rmix.exp(100,c(0.3,0.7),c(2,10))
out <- emtest.exp(x,2)
plotmix.exp(x,out)