sn.mmle {sn} | R Documentation |
Fits a one-dimensional skew-normal (SN) or skew-t (ST) distribution to data, or fits a linear regression model with skew-normal errors, using a modification of maximum likelihood estimation.
sn.mmle(X, y, plot.it=TRUE, trace=FALSE, ...) st.mmle(X, y, df, trace=FALSE)
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 has only one column, then it is assumed to be made of 1's.
Missing values (NA s) are not allowed.
|
df |
a positive real value representing the degrees of freedom, in the ST case |
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 .
|
... |
Additional arguments passed to sn.mle
|
If plotting operates, the function sm.density
of the library sm
is searched. If sm.density
is not found, an histogram is plotted.
from sn.mmle
, a list containing the following components:
call |
a string containing the calling statement |
dp |
a vector of length ncol(X)+2 with estimates of the direct parameters
|
se |
a vector of standard errors for the parameters |
Einfo |
the expected Fisher information matrix for the parameters |
from st.mmle
only the call
and dp
components are returned
Maximum likelihood estimation for SN and ST models can lead to estimates
of the shape parameters on the frontier (that is Inf
for the
DP parameters); see Azzalini and Capitanio (1999) for a discussion
of this aspect in the SN case.
To avoid this situation, an alternative estimation criterion is the
method of Sartori-Firth, which involves first regular maximum estimation
and subsequent re-estimation of the shape parameter using a modified
score function; see the references below for a full discussion.
The effect of this modification is "negligible" for large sample size,
but it avoids estimates of the frontier of the parameter space.
Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579–602.
Firth, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika 80, 27–38. (Corr: 95V82 p.667).
Sartori, N. (2006). Bias prevention of maximum likelihood estimates for scalar skew normal and skew $t$ distributions. J. Statist. Plann. Inf. 136, 4259–4275.
data(ais, package="sn") attach(ais) a <- sn.mmle(y=bmi) # M <- model.matrix(~lbm+sex) b <- sn.mmle(M,bmi)