sn.mle {sn} | R Documentation |
Fits a skew-normal (SN) distribution to data, or fits a linear regression model with skew-normal errors, using maximum likelihood estimation.
sn.mle(X, y, cp, plot.it=TRUE, trace=FALSE, method="L-BFGS-B", control=list(iter.max=100, abs.tol=1e-5))
y |
a vector contaning the observed variable. This is the response
variable in case of linear regression.
Missing values (NA s) are not allowed.
|
X |
a matrix of explanatory variables.
If X is missing, then a one-column matrix of all 1's is created.
If X is supplied, then it must include a column of 1's.
Missing values (NA s) are not allowed.
|
cp |
a vector of initial values for the centred parameters,
with length(cp)=ncol(X)+2
|
plot.it |
logical value, If plot.it=TRUE (default),
a plot of the nonparametric estimate of variable y (or the residuals,
in the case of regression), and the parametric fit is superimposed.
See below for details.
|
trace |
logical value which controls printing of the algorithm convergence.
If trace=TRUE , details are printed. Default value is FALSE .
|
method |
this parameter is just passed to the optimizer optim ; see the
documentation of this function for its usage. Default value is
"L-BFGS-B" . |
control |
this parameter is just passed to the optimizer optim ;
see the documentation of this function for its usage.
|
The optimizer optim
is used, supplying the gradient of the log-likelihood.
Convergence is generally fast and reliable, but inspection of
the returned message
from optim
is always appropriate.
In suspect cases, re-run the function changing the starting cp
vector.
If plotting operates, the function sm.density
of the library sm
is searched; this library is associated with the book by Bowman and
Azzalini (1997). If sm.density
is not found, an histogram is plotted.
a list containing the following components:
call |
a string containing the calling statement |
cp |
a vector of length ncol(X)+2 with the centred parameters
|
logL |
the log-likelihood at convergence |
se |
a vector of standard errors for the cp component
|
info |
the observed information matrix for the cp component
|
optim |
the list returned by the optimizer optim ; see the documentation
of this function for explanation of its components.
|
If plot.it=TRUE
and a graphical device is active, a plot is produced,
as described above.
Background information on the SN distribution is given by Azzalini (1985). See Azzalini and Capitanio (1999) for a more detailed discussion of the centred parametrization.
Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178.
Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579–602.
Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis: the Kernel Approach with S-Plus Illustrations. Oxford University Press, Oxford.
dsn
, sn.em
, msn.mle
,
optim
, sn.mmle
, sn.mle.grouped
data(ais, package="sn") attach(ais) a<-sn.mle(y=bmi) # a<-sn.mle(X=cbind(1,lbm),y=bmi) # b<-sn.mle(X=model.matrix(~lbm+sex), y=bmi)