sn (version 0.30)

sn.mle: Maximum likelihood estimation for skew-normal models

Description

Fits a skew-normal (SN) distribution to data, or fits a linear regression model with skew-normal errors, using maximum likelihood estimation.

Usage

sn.mle(X, y, cp, plotit=TRUE, trace=FALSE, method="L-BFGS-B",
          control=list(iter.max=100, abs.tol=1e-5))

Arguments

y

a vector contaning the observed variable. This is the response variable in case of linear regression. Missing values (NAs) 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, and an intercept term is required, then it must include a column of 1's. Missing values (NAs) are

cp

a vector of initial values for the centred parameters, with length(cp)=ncol(X)+2

plotit

logical value, If plotit=TRUE (default) and a graphical device is active, 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 det

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.

Value

• 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.

Side Effects

If plotit=TRUE and a graphical device is active, a plot is produced, as described above.

Background

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.

Details

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.

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.

Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis: the Kernel Approach with S-Plus Illustrations. Oxford University Press, Oxford.

See Also

dsn, sn.em, msn.mle, optim

Examples

data(ais,package=sn)
attach(ais)
a<-sn.mle(y=bmi)
#
a<-sn.mle(X=cbind(1,lbm,lbm^2),y=bmi)
#
M<-model.matrix(~lbm+I(ais$sex))
b<-sn.mle(M,bmi)