sn (version 0.4-3)

sn.mmle: Modified maximum likelihood estimation for skew-normal ans skew-t models

Description

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

Usage

sn.mmle(X, y, plot.it=TRUE, trace=FALSE, ...)
st.mmle(X, y, df, trace=FALSE)

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 has only one column, then it is assumed to be made of 1's. Missing values (NAs) are not allowed.

df

a positive real value representing the degrees of freedom, in the ST case

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.

...

Additional arguments passed to sn.mle

Value

• from sn.mmle, a list containing the following components:
• call
  a string containing the calling statement
• dp
  a vector of length ncol(X)+2 with estimates of the direct parameters
• se
  a vector of standard errors for the parameters
• Einfo
  the expected Fisher information matrix for the parameters
• from st.mmle only the call and dp components are returned

Background

Maximum likelihood estimation for SN and ST models can lead to estimates of the shape parameters on the frontier (that is Inf for the DP parameters); see Azzalini and Capitanio (1999) for a discussion of this aspect in the SN case. To avoid this situation, an alternative estimation criterion is the method of Sartori-Firth, which involves first regular maximum estimation and subsequent re-estimation of the shape parameter using a modified score function; see the references below for a full discussion. The effect of this modification is "negligible" for large sample size, but it avoids estimates of the frontier of the parameter space.

Details

If plotting operates, the function sm.density of the library sm is searched. If sm.density is not found, an histogram is plotted.

References

Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579--602.

Firth, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika 80, 27--38. (Corr: 95V82 p.667).

Sartori, N. (2006). Bias prevention of maximum likelihood estimates for scalar skew normal and skew $t$ distributions. J. Statist. Plann. Inf. 136, 4259--4275.

See Also

sn.mle, sn.Einfo

Examples

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