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())mst.mle) or a vector (for st.mle).
If y is a matrix, rows refer to observations, and columns to
components of the multivariate distribution.y.
If X is supplied, then it must include a column of 1's.y.mst.mle, a list contaning the components
beta,Omega, alpha,
df of the type described below; for st.mle, a vector whose
components contain analogous ingredients as before, with the exception
that the scale parameter is the square root of Omega. In both
cases, the dp component of the returned list from a previous call
has the required format and it can be used as a new start. If the
start parameter is missing, initial values are selected by the
function.NA (default value) if df is a parameter
to be estimated.trace=TRUE, details are printed. Default value is FALSE."nlminb", then this function is called; in all other cases,
optim is called, with method set equal to the given string.
Default value is "nlminb".nlminb
or optim; see the documentation of this function for its usage.mst.mle, this is a list containing the direct parameters
beta, Omega, alpha.
Here, beta is a matrix of regression coefficients with
dim(beta)=c(ncol(X),ncol(y)), Omega is a covariance matrix
of order ncol(y), alpha is a vector of shape parameters of
length ncol(y). For st.mle, dp is a vector of
length ncol(X)+3, containing c(beta, omega, alpha, df), where
omega is the square root of Omega.beta, alpha, info.
Here, beta and alpha are the standard errors for the
corresponding point estimates;
info is the observed information matrix for the working parameter,
as explained below.nlminb
or optim, plus an item with the name of the selected
algorithm; see the documentation of either nlminb
or optim for explanation of the other components.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.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).
dstdat <- rt(100, df=5, ncp=100)
fit <- st.mle(y=dat)
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