mst.mle(sn)
mst.mle()所属R语言包：sn
Maximum likelihood estimation for a (multivariate) skew-t distribution
（多元）偏斜t分布的最大似然估计
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Fits a skew-t (ST) or multivariate skew-t (MST) distribution to data, or fits a linear regression model with (multivariate) skew-t errors, using maximum likelihood estimation.
适用于歪斜-T（ST）或多元歪斜-T（MST）分布的数据，或，适合线性回归模型（多元）歪斜-T的错误，用最大似然估计。
用法----------Usage----------
mst.mle(X, y, freq, start, fixed.df=NA, trace=FALSE,
algorithm = c("nlminb","Nelder-Mead", "BFGS", "CG", "SANN"), control=list())
st.mle(X, y, freq, start, fixed.df=NA, trace=FALSE,
algorithm = c("nlminb","Nelder-Mead", "BFGS", "CG", "SANN"), control=list())
参数----------Arguments----------
参数：y
a matrix (for mst.mle) or a vector (for st.mle). If y is a matrix, rows refer to observations, and columns to components of the multivariate distribution.
一个矩阵（mst.mle）或一个向量（st.mle）。如果y是一个矩阵，行观察，和多变量分布列的组成部分。
参数：X
a matrix of covariate values. If missing, a one-column matrix of 1's is created; otherwise, it must have the same number of rows of y. If X is supplied, then it must include a column of 1's.
矩阵的协变量值。如果缺少，矩阵中1的一列被创建，否则，它必须有相同数量的行y。如果X提供，那么它必须包含一列1。
参数：freq
a vector of weights. If missing, a vector of 1's is created; otherwise it must have length equal to the number of rows of y.
的权重的矢量。如果缺少，创建的向量1的，否则，它必须有y的数量的行的长度相等。
参数：start
for mst.mle, a list contaning the components beta,Omega, alpha, df of the type described below; for st.mle, a vector whose components contain analogous ingredients as before, with the exception that the scale parameter is the square root of Omega. In both cases, the dp component of the returned list from a previous call has the required format and it can be used as a new start. If the start parameter is missing, initial values are selected by the function.
mst.mle，浸渗的组件列表beta，Omega，alpha，df下面所描述的类型;st.mle，一个向量其成分含有类似成分和以前一样，除尺度参数的平方根Omega。在这两种情况下，dp分量的前一呼叫的返回的列表从具有所需的格式，它可被用作一个新的start。如果start参数丢失，初始值选择由该函数。
参数：fixed.df
a scalar value containing the degrees of freedom (df), if these must be taked as fixed, or NA (default value) if df is a parameter to be estimated.
标量值的自由度（DF），如果这些都必须抽放固定，或NA（默认值），如果df是一个参数进行估计。
参数：trace
logical value which controls printing of the algorithm convergence. If trace=TRUE, details are printed. Default value is FALSE.
逻辑控制打印算法的收敛值。如果trace=TRUE，细节被打印出来。默认值为FALSE。
参数：algorithm
a character string which selects the numerical optimization procedure used to maximize the loglikelihood function. If this string is set equal to "nlminb", then this function is called; in all other cases, optim is called, with method set equal to the given string. Default value is "nlminb".
选择的数值的的优化过程用于最大化loglikelihood功能，一个字符串。如果该字符串等于"nlminb"，那么这个函数将被调用;在所有其他情况下，optim被称为，method设置为等于给定的字符串。默认值为"nlminb"。
参数：control
this parameter is passed to the chose optimizer, either nlminb or optim; see the documentation of this function for its usage. </table>
这个参数被传递到选择的优化，是nlminb或optim其使用此功能，请参阅文档。 </ TABLE>
Details
详细信息----------Details----------
If y is a vector and it is supplied to mst.mle, then it is converted to a one-column matrix, and a scalar skew-t distribution is fitted. This is also the mechanism used by st.mle which is simply an interface to mst.mle.
如果y是一个向量，它被提供给mst.mle，则它被转换成一列的矩阵，以及一个标量嵌合歪斜-t分布。这也是st.mle这是一个简单的接口，mst.mle使用的机制。
The parameter freq is intended for use with grouped data, setting the values of y equal to the central values of the cells; in this case the resulting estimate is an approximation to the exact maximum likelihood estimate. If freq is not set, exact maximum likelihood estimation is performed.
参数freq被用于与分组数据一起使用，设置y等于单元的中心值的值，在这种情况下，将所得的估计是一个近似的精确的最大似然估计。 freq如果没有设置，精确极大似然估计。
Numerical search of the maximum likelihood estimates is performed in a suitable re-parameterization of the original parameters with aid of the selected optimizer (nlminb or optim) which is supplied with the derivatives of the log-likelihood function. Notice that, in case the optimizer is optim), the gradient may or may not be used, depending on which specific method has been selected. On exit from the optimizer, an inverse transformation of the parameters is performed. For a specific description on the re-parametrization adopted, see Section 5.1 and Appendix B of Azzalini \& Capitanio (2003).
搜索最大似然估计的数值是在一个合适的再衍生工具的对数似然函数的参数提供的援助选定的优化与原来的参数（nlminb或optim） 。请注意的是，在情况下，优化器是optim），梯度可能会或可能不会被使用，取决于已选择特定的方法。在退出的优化，逆变换的参数。重新参数化采用的具体描述，请参见第5.1节和附录B Azzalini \＆卡皮塔尼奥（2003年）。
值----------Value----------
A list containing the following components:
一个列表，其中包含以下组件：
<table summary="R valueblock"> <tr valign="top"><td>call</td> <td> a string containing the calling statement. </td></tr> <tr valign="top"><td>dp</td> <td> for mst.mle, this is a list containing the direct parameters beta, Omega, alpha. Here, beta is a matrix of regression coefficients with dim(beta)=c(ncol(X),ncol(y)), Omega is a covariance matrix of order ncol(y), alpha is a vector of shape parameters of length ncol(y). For st.mle, dp is a vector of length ncol(X)+3, containing c(beta, omega, alpha, df), where omega is the square root of Omega. </td></tr> <tr valign="top"><td>se</td> <td> a list containing the components beta, alpha, info. Here, beta and alpha are the standard errors for the corresponding point estimates; info is the observed information matrix for the working parameter, as explained below. </td></tr> <tr valign="top"><td>algorithm</td> <td> the list returned by the chose optimizer, either nlminb or optim, plus an item with the name of the selected algorithm; see the documentation of either nlminb or optim for explanation of the other components. </td></tr></table>
<table summary="R valueblock"> <tr valign="top"> <TD>call</ TD> <td>一个字符串，其中包含调用语句。 </ TD> </ TR> <tr valign="top"> <TD> dp </ TD> <TD>mst.mle，这是一个列表，其中包含的直接参数beta ，Omega，alpha。在这里，beta是一个矩阵的回归系数与dim(beta)=c(ncol(X),ncol(y))，Omega的协方差矩阵为了ncol(y)，alpha是一个矢量形状参数的长度ncol(y)。对于st.mle，dp是一个向量的长度ncol(X)+3，包含c(beta, omega, alpha, df)，其中omega是的平方根Omega。 </ TD> </ TR> <tr valign="top"> <TD> se</ TD> <td>一个列表，其中包含的组件beta，alpha，info。在这里，beta和alpha的对应点的标准误差的估计;info是观察到的信息矩阵的工作参数，如下面解释。 </ TD> </ TR> <tr valign="top"> <TD>algorithm </ TD> <TD>列表中返回所选择的优化，无论是nlminb或optim ，加上一个资料与name选定的算法;看到的文档的任nlminb或optim用于说明的其他组件。 </ TD> </ TR> </ TABLE>
背景----------Background----------
The family of multivariate skew-t distributions is an extension of the multivariate Student's t family, via the introduction of a shape parameter which regulates skewness; when shape=0, the skew-t distribution reduces to the usual t distribution. When df=Inf the distribution reduces to the multivariate skew-normal one; see dmsn. See the reference below for additional information.
多变量偏斜t分布的家庭是一个扩展的多元学生的T系列，通过引进一个shape参数调节偏度;当shape=0，歪斜-t分布的降低通常吨分布。当df=Inf分布减少到多变量的偏移正常的;看到dmsn。下面的其他信息，请参阅参考。
参考文献----------References----------
Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. The full version of the paper published in abriged form in J.Roy. Statist. Soc. B 65, 367–389, is available at http://azzalini.stat.unipd.it/SN/se-ext.ps
参见----------See Also----------
dmst,msn.mle,mst.fit, nlminb, optim
dmst，msn.mle，mst.fit，nlminb，optim
实例----------Examples----------
data(ais, package="sn")
attach(ais)
X.mat <- model.matrix(~lbm+sex)
b <- sn.mle(X.mat, bmi)
# []
b <- mst.mle(y=cbind(Ht,Wt))
#[]
# a multivariate regression case:[多元回归的情况下：]
a <- mst.mle(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-6))
#[]
# refine the previous outcome[改进了先前的结果]
a1 <- mst.mle(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-9), start=a$dp)
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
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发表于 2012-9-30 11:19:38
