mst.mle {doppelgangR} | R Documentation |
Fits a skew-t (ST) or multivariate skew-t (MST) distribution to data, or
fits a linear regression model with (multivariate) skew-t errors,
using maximum likelihood estimation. Functions copied from sn
CRAN library v0.4.18 because they were later deprecated in that library.
mst.mle(X, y, freq, start, fixed.df=NA, trace=FALSE, algorithm = c("nlminb","Nelder-Mead", "BFGS", "CG", "SANN"), control=list()) st.mle(X, y, freq, start, fixed.df=NA, trace=FALSE, algorithm = c("nlminb","Nelder-Mead", "BFGS", "CG", "SANN"), control=list())
y |
a matrix (for |
X |
a matrix of covariate values.
If missing, a one-column matrix of 1's is created; otherwise,
it must have the same number of rows of |
freq |
a vector of weights.
If missing, a vector of 1's is created; otherwise
it must have length equal to the number of rows of |
start |
for |
fixed.df |
a scalar value containing the degrees of freedom (df), if these must
be taked as fixed, or |
trace |
logical value which controls printing of the algorithm convergence.
If |
algorithm |
a character string which selects the numerical optimization procedure
used to maximize the loglikelihood function. If this string is set
equal to |
control |
this parameter is passed to the chose optimizer, either |
If y
is a vector and it is supplied to mst.mle
, then
it is converted to a one-column matrix, and a scalar skew-t distribution
is fitted. This is also the mechanism used by st.mle
which is simply an interface to mst.mle
.
The parameter freq
is intended for use with grouped data,
setting the values of y
equal to the central values of the
cells; in this case the resulting estimate is an approximation
to the exact maximum likelihood estimate. If freq
is not
set, exact maximum likelihood estimation is performed.
Numerical search of the maximum likelihood estimates is performed in a
suitable re-parameterization of the original parameters with aid of the
selected optimizer (nlminb
or optim
) which is supplied
with the derivatives of the log-likelihood function. Notice that, in
case the optimizer is optim
), the gradient may or may not be
used, depending on which specific method has been selected. On exit
from the optimizer, an inverse transformation of the parameters is
performed. For a specific description on the re-parametrization adopted,
see Section 5.1 and Appendix B of Azzalini \& Capitanio (2003).
A list containing the following components:
call |
a string containing the calling statement. |
dp |
for |
se |
a list containing the components |
algorithm |
the list returned by the chose optimizer, either |
The family of multivariate skew-t distributions is an extension of the
multivariate Student's t family, via the introduction of a shape
parameter which regulates skewness; when shape=0
, the skew-t
distribution reduces to the usual t distribution.
When df=Inf
the distribution reduces to the multivariate skew-normal
one; see dmsn
. See the reference below for additional information.
Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. The full version of the paper published in abriged form in J.Roy. Statist. Soc. B 65, 367–389, is available at http://azzalini.stat.unipd.it/SN/se-ext.ps
dat <- rt(100, df=5, ncp=100) fit <- st.mle(y=dat) fit