tM {ICS} | R Documentation |
The functions implements three EM algorithms to M-estimate the location vector and scatter matrix of a multivariate t-distribution.
tM(X, df = 1, alg = "alg3", mu.init = NULL, V.init = NULL, gamma.init = NULL, eps = 1e-06, maxiter = 100, na.action = na.fail)
X |
numeric data matrix or dataframe. |
df |
assumed degrees of freedom of the t-distribution. Default is 1 which corresponds to the Cauchy distribution. |
alg |
specifies which algorithm to use. Options are alg1 , alg2 or alg3 . alg3 is the default. |
mu.init |
initial value for the location vector if available. |
V.init |
initial value for the scatter matrix if available. |
gamma.init |
initial value for gamma if available. Only needed for alg2 . |
eps |
convergence tolerance. |
maxiter |
maximum number of iterations. |
na.action |
a function which indicates what should happen when the data contain 'NA's. Default is to fail. |
This implements the EM algorithms described in Kent et al. (1994). The norm used to define convergence is as in Arslan et al. (1995).
Algorithm 1 is valid for all degrees of freedom df
> 0. Algorithm 2 is well defined only for degrees of freedom df
> 1.
Algorithm 3 is the limiting case of Algorithm 2 with degrees of freedom df
= 1.
The performance of the algorithms are compared in Arslan et al. (1995).
Note that cov.trob
in the MASS package implements also a covariance estimate for a multivariate t-distribution.
That function provides for example also the possibility to fix the location. It requires however that the degrees of freedom exceeds 2.
A list containing:
mu |
vector with the estimated loaction. |
V |
matrix of the estimated scatter. |
gam |
estimated value of gamma. Only present when alg2 is used. |
iter |
number of iterations. |
Klaus Nordhausen, klaus.nordhausen@uta.fi
Kent, J.T., Tyler, D.E. and Vardi, Y. (1994), A curious likelihood identity for the multivariate t-distribution, Communications in Statistics, Theory and Methods, 23, 441–453.
Arslan, O., Constable, P.D.L. and Kent, J.T. (1995), Convergence behaviour of the EM algorithm for the multivariate t-distribution, Communications in Statistics, Theory and Methods, 24, 2981–3000.
set.seed(654321) cov.matrix <- matrix(c(3,2,1,2,4,-0.5,1,-0.5,2), ncol=3) X <- rmvt(100, cov.matrix, 1) tM(X) rm(.Random.seed)