The functions implements three EM algorithms to M-estimate the location vector and scatter matrix of a multivariate t-distribution.
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X |
numeric data matrix or dataframe. |
df |
assumed degrees of freedom of the t-distribution. Default is |
alg |
specifies which algorithm to use. Options are |
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 |
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 |
iter |
number of iterations. |
Klaus Nordhausen
Kent, J.T., Tyler, D.E. and Vardi, Y. (1994), A curious likelihood identity for the multivariate t-distribution, Communications in Statistics, Simulation and Computation, 23, 441–453. <doi:10.1080/03610919408813180>.
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. <doi:10.1080/03610929508831664>.
cov.trob
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