mixtools (version 0.3.0)

spEMsymloc: Semiparametric EM-like Algorithm for univariate symmetric location mixture

Description

Returns semiparametric EM algorithm output (Bordes et al, 2007, and Benaglia et al, 2007) for location mixtures of univariate data and symmetric component density.

Usage

spEMsymloc(x, mu0, bw = bw.nrd0(x), h=bw, eps = 1e-8, maxiter = 100, 
    stochastic = FALSE, verb = TRUE)

Arguments

x

A vector of length $n$ consisting of the data.

mu0

Either a vector specifying the initial centers for the kmeans function, and from which the number of component is obtained, or an integer $m$ specifying the number of initial centers, which are then cho

bw

Bandwidth for density estimation, equal to the standard deviation of the kernel density.

h

Alternative way to specify the bandwidth, to provide backward compatibility.

eps

Tolerance limit for declaring algorithm convergence. Convergence is declared before maxiter iterations whenever the maximum change in any coordinate of the lambda (mixing proportion estimates) and mu (means)

maxiter

The maximum number of iterations allowed, for both stochastic and non-stochastic versions; for non-stochastic algorithms (stochastic = FALSE), convergence may be declared before maxiter iterations (see eps ab

stochastic

Flag, if FALSE (the default), runs the non-stochastic version of the algorithm, as in Benaglia et al (2007). Set to TRUE to run a stochastic version which simulates the posteriors at each iteration (as in Bordes et al, 2007), and runs

verb

If TRUE, print updates for every iteration of the algorithm as it runs

Value

• spEMsymloc returns a list of class npEM with the following items:
• data
  The raw data (an $n\times r$ matrix).
• posteriors
  An $n\times m$ matrix of posterior probabilities for observations. If stochastic = TRUE, this matrix is computed from an average over the maxiter iterations.
• bandwidth
  Same as the bw input argument, returned because this information is needed by any method that produces density estimates from the output.
• lambda
  The sequence of mixing proportions over iterations.
• lambdahat
  The final estimate for mixing proportions if stochastic = FALSE, the average over the sequence if stochastic = TRUE.
• mu
  the sequence of component means over iterations.
• muhat
  the final estimate of component means if stochastic = FALSE, the average over the sequence if stochastic = TRUE.
• symmetric
  Flag indicating that the kernel density estimate is using a symmetry assumption.

References

\itemBordes, L., Chauveau, D., and Vandekerkhove, P. (2007), An EM algorithm for a semiparametric mixture model, Computational Statistics and Data Analysis, 51: 5429-5443.

\itemBenaglia, T., Chauveau, D., and Hunter, D. R. (2007), An EM-like algorithm for semi- and non-parametric estimation in multivariate mixtures, Penn State Department of Statistics Technical Report 07-01.

See Also

plot.npEM, rnormmix, npEMindrep, plotseq.npEM

Examples

## Example from a normal location mixture
n<-200
lambda <- c(1/3,2/3)
mu<-c(0, 4); sigma<-rep(1, 2)
x <- rnormmix(n, lambda, mu, sigma)
out.stoc <- spEMsymloc(x, mu0=c(-1, 2), stochastic=TRUE)
out.nonstoc <- spEMsymloc(x, mu0=c(-1, 2))