summary
method for class "selm"
and "mselm"
.
1 2 3 4 5 
object 
an object of class 
param.type 
a character string which indicates the required type of
parameter type; possible values are 
cov 
a logical value, to indicate if an estimate of the variance and
covariance matrix of the estimates is required (default: 
cor 
a logical value, to indicate if an estimate of the correlation
matrix of the estimates is required (default: 
An S4 object of class summary.selm
with 12 slots.

the calling statement. 

the parametric family of skewellitically contoured distributed (SEC) type. 

the maximized loglikelihood or penalized loglikelihood value 

estimation method ( 

a characer string with the chosen parameter set. 

table of parameters, std.errors and zvalues 

a list of fixed parameter values 

residual values 

a list with control parameters 

a list of auxiliary quantities 

a numeric vector with various lengths and dimensions 

a logical value which indicates whether the estimates are on the boundary of the parameter space 
There are two reasons why the default choice of param.type
is
CP
. One is the the easier interpretation of cumulantbased quantities
such as mean value, standard deviation, coefficient of skewness.
The other reason is more technical and applies only to cases when the
estimate of the slant parameter alpha of the SN distribution
is close to the origin: standard asymptotic distribution theory of maximum
likelihood estimates (MLE's) does not apply in this case and the
corresponding standard errors are not trustworthy.
The problem is especialy severe at
α=0 but to some extent propagates to its vicinity.
If d=1, adoption of CP
leads to MLE's with regular asymptotic
distribution across the parameter space, including α=0.
For d>1 and α=0, the problem is still unsolved at the
present time, which is the reason why selm
issues a warning
message when the MLE is in the vicinity of α=0;
see ‘Details’ of selm
.
For background information, see Sections 3.1.4–6 and 5.2.3 of
Azzalini and Capitanio (2014) and references therein.
This problem does not occur with the the SC and the ST
distribution (unless its tailweight parameter nu
diverges, that is,
when we are effectively approaching the SN
case).
Adelchi Azzalini
Azzalini, A. with the collaboration of Capitanio, A. (2014). The SkewNormal and Related Families. Cambridge University Press, IMS Monographs series.
selm
function,
selm
(and mselm
) class,
plot.selm
, dp2cp
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data(wines, package="sn")
m5 < selm(acidity ~ phenols + wine, family="SN", data=wines)
summary(m5)
summary(m5, "dp")
s5 < summary(m5, "dp", cor=TRUE, cov=TRUE)
dp.cor < slot(s5, "aux")$param.cor
cov2cor(vcov(m5, "dp")) # the same
#
# m6 < selm(acidity ~ phenols + wine, family="ST", data=wines) # boundary!?
#
m12 < selm(cbind(acidity, alcohol) ~ phenols + wine, family="SN", data=wines)
s12 < summary(m12)
coef(m12, 'dp')
coef(m12, "dp", vector=FALSE)
#
# see other examples at function selm

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