MixtureInf (version 1.0-1)

emtest.norm: Likelihood-based testing for the order of a finite mixture of normals

Description

Tests the order of a finite mixture of normals with univariate mixing parameter. The variance for each component is assumed to be 1.

Usage

emtest.norm(x, m0, C = NULL, len = 5, eps = 1e-05)

Arguments

x

observations whose order is being tested: vector or a matrix with the 1st column being the observed values and the 2nd column being the corresponding frequency.

m0

order under null hypothesis

C

optional tuning parameter for EM-test procedure (if not provided, it will be determined by the formulas described in Chen and Li, 2011)

len

the number of random restarts of the EM-algorithm

eps

tolerance value for the convergence of the EM-algorithm

Value

• Returns an object of class emtest with the following elements:
• family
  'normal'
• m0
  order of the mixture
• alpha
  estimated mixing proportions
• theta
  estimated component parameters
• C
  tuning parameter used
• ah
  estimated weights in the $\chi^2$ mixture-limiting distribution
• emstat
  EM-test statistics
• pvalue
  p-values of the EM test statistics

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

emtest.binom, emtest.exp, emtest.norm, emtest.pois

Examples

x <- rnormmix(200, c(0.5, 0.5), c(-2, 2))
  emtest.norm(x, 2)