sn (version 0.4-18)

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, plot.it=TRUE, trace=FALSE, method="L-BFGS-B",
          control=list(maxit=100))

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, then it must include a column of 1's. Missing values (NAs) are not allowed.

cp

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

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.

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 plot.it=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 also Azzalini and Capitanio (1999), for an additional 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 package 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.

To fit a skew-normal distribution to grouped data by exact maximum likelihood estimation, use sn.mle.grouped.

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, sn.mmle, sn.mle.grouped

Examples

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