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Maximum likelihood estimation for skew-normal models
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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 maximum likelihood estimation.
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sn.mle(X, y, cp, plot.it=TRUE, trace=FALSE, method="L-BFGS-B",
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control=list(maxit=100))
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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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Missing values (\code{NA}s) are not allowed.
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a matrix of explanatory variables.
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If \code{X} is missing, then a one-column matrix of all 1's is created.
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If \code{X} is supplied, then it must include a column of 1's.
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Missing values (\code{NA}s) are not allowed.
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a vector of initial values for the centred parameters,
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with \code{length(cp)=ncol(X)+2}
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logical value, If \code{plot.it=TRUE} (default),
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a plot of the nonparametric estimate of variable \code{y} (or the residuals,
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in the case of regression), and the parametric fit is superimposed.
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See below for details.
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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{FALSE}.
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this parameter is just passed to the optimizer \code{optim}; see the
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documentation of this function for its usage. Default value is
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this parameter is just passed to the optimizer \code{optim};
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see the documentation of this function for its usage.
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a list containing the following components:
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a string containing the calling statement
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a vector of length \code{ncol(X)+2} with the centred parameters
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the log-likelihood at convergence
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a vector of standard errors for the \code{cp} component
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the observed information matrix for the \code{cp} component
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the list returned by the optimizer \code{optim}; see the documentation
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of this function for explanation of its components.
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\section{Side Effects}{
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If \code{plot.it=TRUE} and a graphical device is active, a plot is produced,
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The optimizer \code{optim} is used, supplying the gradient of the log-likelihood.
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Convergence is generally fast and reliable, but inspection of
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the returned \code{message} from \code{optim} is always appropriate.
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In suspect cases, re-run the function changing the starting \code{cp}
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If plotting operates, the function \code{sm.density} of the package \code{sm}
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is searched; this library is associated with the book by Bowman and
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Azzalini (1997). If \code{sm.density} is not found, an histogram is plotted.
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To fit a skew-normal distribution to grouped data by exact maximum likelihood
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estimation, use \code{sn.mle.grouped}.
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Background information on the SN distribution is given by Azzalini (1985).
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See also Azzalini and Capitanio (1999), for an additional discussion of
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the centred parametrization.
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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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Bowman, A.W. and Azzalini, A. (1997).
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\emph{Applied Smoothing Techniques for Data Analysis:}
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\emph{the Kernel Approach with S-Plus Illustrations.}
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Oxford University Press, Oxford.
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\code{\link{dsn}}, \code{\link{sn.em}}, \code{\link{msn.mle}},
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\code{\link{optim}}, \code{\link{sn.mmle}}, \code{\link{sn.mle.grouped}}
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data(ais, package="sn")
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a<-sn.mle(X=cbind(1,lbm),y=bmi)
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b<-sn.mle(X=model.matrix(~lbm+sex), y=bmi)
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\keyword{distribution}
added
removed
man/sn.mle.Rd
