sn (version 0.4-18)

sn.Einfo: Expected Fisher information for SN distribution parameters

Description

Computes expected Fisher information for parameters of simple sample having one-dimensional skew-normal (SN) distribution or regression model having SN errors, in the DP and CP parametrizations.

Usage

sn.Einfo(dp=NULL, cp=NULL, n=1, x=NULL)

Arguments

dp, cp

vector of direct or centred parameters, respectively; one of the two vectors must be supplied, but not both. See below for more details.

n

sample size; if this parameter is supplied, then x must not be.

x

design matrix of the regression model; if this parameter is supplied, then n must not be.

Value

• a list containing the following components:
• dp, cp
  DP and CP parameters; one of the two vectors is the one supplied on input, the other one matches the previous one in the alternative parametrization
• info.dp, info.cp
  matrices of Fisher expected information in the two parametrizations
• se.dp, se.cp
  vectors of standard errors in the two parametrizations
• aux
  a list containing two elements: (1) a matrix D of derivatives of DP parameters with respect to CP parameters, (2) a vector a.int which contains the coefficients a0, a1, a2 described in the reference below.

Details

When x is not set, then a simple random sample is assumed and a matrix x with a single column of all 1's is constructed; in this case, the supplied vector dp or cp must have length 3. If x is set, then the supplied vector of parameters must have length ncol(x)+2.

Background

For the description of the DP and CP parametrizations and for the expression of the expected Fisher information of the DP parametrizations, see Azzalini (1985). Further discussion is given by Azzalini and Capitanio (1999).

References

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.

See Also

dsn, cp.to.dp, dp.to.cp

Examples

info <- sn.Einfo(dp=c(0,1,5), n=3)
#
data(ais, package="sn")
M <- model.matrix(~ais$"Ht")
mle <- sn.mle(X=M, y=ais$"Wt", plot.it=FALSE)
info <- sn.Einfo(cp=mle$cp, x=M)