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Fitting Skew-normal variables using the EM algorithm
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Fits a skew-normal (SN) distribution to data, or fits a linear regression
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model with skew-normal errors, using the EM algorithm to locate the MLE
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estimate. The estimation procedure can be global or it can fix some
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components of the parameters vector.
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sn.em(X, y, fixed, p.eps=0.0001, l.eps=0.01, trace=FALSE, data=FALSE)
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a vector contaning the observed variable. This is the response
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variable in case of linear regression.
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a matrix of explanatory variables. If \code{X} is missing, then a one-column
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matrix of all 1's is created. If \code{X} is supplied, and an intercept term
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is required, then it must include a column of 1's.
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a vector of length 3, indicating which components of the
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parameter vector must be regarded as fixed. In \code{fixed=c(NA,NA,NA)},
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which is the default setting, a global maximization is performed.
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If the 3rd component is given a value, then maximization is performed
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keeping that value fixed for the shape parameter. If the 3rd and 2nd
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parameters are fixed, then the scale and the shape parameter are
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kept fixed. No other patterns of the fixed values are allowed.
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numerical value which regulates the parameter convergence tolerance.
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numerical value which regulates the log-likelihood convergence tolerance.
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logical value which controls printing of the algorithm convergence.
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If \code{trace=TRUE}, details are printed. Default value is \code{F}.
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logical value. If \code{data=TRUE}, the returned list includes the original
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data. Default value is \code{data=FALSE}.
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a list with the following components:
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a vector of the direct parameters, as explained in the references below.
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a vector of the centred parameters, as explained in the references below.
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the log-likelihood at congergence.
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optionally (if \code{data=TRUE}), a list containing \code{X} and \code{y,} as supplied
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on input, and a vector of \code{residuals}, which should have an approximate
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SN distribution with \code{location=0} and \code{scale=1}, in the direct
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The function works using the direct parametrization; on convergence,
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the output is then given in both parametrizations.
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This function is based on the EM algorithm; it is generally quite slow,
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but it appears to be very robust.
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See \code{sn.mle} for an alternative method, which also returns standard
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Background information on the SN distribution is given by Azzalini (1985).
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See Azzalini and Capitanio (1999) for a more detailed discussion of
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the direct and centred parametrizations.
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A class of distributions which includes the normal ones.
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\emph{Scand. J. Statist.}
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Azzalini, A. and Capitanio, A. (1999).
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Statistical applications of the multivariate skew-normal distribution.
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\emph{J.Roy.Statist.Soc. B}
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\code{\link{dsn}}, \code{\link{sn.mle}}, \code{\link{cp.to.dp}}
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data(ais, package="sn")
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a<-sn.em(X=cbind(1,lbm,lbm^2),y=bmi)
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M<-model.matrix(~lbm+I(ais$sex))
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fit <- sn.em(y=bmi, fixed=c(NA, 2, 3), l.eps=0.001)
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\keyword{distribution}
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