Qpenalty {sn} | R Documentation |
selm
modelsPenalty function for the log-likelihood of selm
models
when method="MPLE"
. Qpenalty
is the default function;
MPpenalty
is an example of a user-defined function effectively
corresponding to a prior distributio on alpha
.
Qpenalty(alpha_etc, nu = NULL, der = 0) MPpenalty(alpha, der = 0)
alpha_etc, alpha |
in the univariate case, a single value |
nu |
degrees of freedom, only required if |
der |
a numeric value in the set 0,1,2 which indicates the
required numer of derivatives of the function. In the multivariate case
the function will only be called with |
The penalty is a function of alpha
, but its expression may
depend on other ingredients, specifically nu
and cov2cor(Omega)
.
See ‘Details’ of selm
for additional information.
The penalty mechanism allows to introduce a prior distribution π for α by setting Q=-log(π), leading to a maximum a posteriori estimate in the stated sense.
As an illustration of this mechanism, function MPpenalty
implements the
‘matching prior’ distribution for the univariate SN distribution
studied by Cabras et al. (2012); their proposal is summarized in
Section 3.2 of Azzalini and Capitanio (2014). Note that, besides
alpha=+/-Inf
, this choice also penalizes alpha=0
with
Q=Inf
, effectively removing alpha=0
from the parameter space.
A positive number Q
representing the penalty, possibly
with attributes attr(Q, "der1")
and attr(Q, "der2")
,
depending onthe input value der
.
Adelchi Azzalini
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.
Cabras, S., Racugno, W., Castellanos, M. E., and Ventura, L. (2012). A matching prior for the shape parameter of the skew-normal distribution. Scand. J. Statist. 39, 236–247.
selm
function
data(frontier) m2 <- selm(frontier ~ 1) m2a <- selm(frontier ~ 1, method="MPLE") m2b <- selm(frontier ~ 1, method="MPLE", penalty="MPpenalty")