R语言 VineCopula包 BiCopEst()函数中文帮助文档(中英文对照)

loveR · 发表于 2012-10-1 16:09:07

BiCopEst(VineCopula)
BiCopEst()所属R语言包：VineCopula

 Parameter estimation for bivariate copula data using inversion of Kendall's tau or maximum likelihood estimation
 二元Copula的数据，用反转的Kendall的tau或最大似然估计的参数估计

 译者：生物统计家园网机器人LoveR

描述----------Description----------

This function estimates the parameter(s) for a bivariate copula using either inversion of empirical Kendall's tau for single parameter copula families or maximum likelihood estimation for one and two parameter copula families supported in this package.
这个函数的参数估计（S）的二元Copula函数可以使用反转的经验Kendall的tau单一参数Copula的家庭的最大似然估计为1和2参数Copula的家庭的支持这个包的。

用法----------Usage----------

BiCopEst(u1, u2, family, method="mle", se=FALSE, max.df=30,
 max.BB=list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1)))

参数----------Arguments----------

参数：u1,u2
Data vectors of equal length with values in [0,1].
数据向量长度相等的值在[0,1]。

参数：family
An integer defining the bivariate copula family: 0 = independence copula 1 = Gaussian copula 2 = Student t copula (t-copula) 3 = Clayton copula 4 = Gumbel copula 5 = Frank copula 6 = Joe copula 7 = BB1 copula 8 = BB6 copula 9 = BB7 copula 10 = BB8 copula 13 = rotated Clayton copula (180 degrees; “survival Clayton”) 14 = rotated Gumbel copula (180 degrees; “survival Gumbel”) 16 = rotated Joe copula (180 degrees; “survival Joe”) 17 = rotated BB1 copula (180 degrees; “survival BB1”) 18 = rotated BB6 copula (180 degrees; “survival BB6”) 19 = rotated BB7 copula (180 degrees; “survival BB7”) 20 = rotated BB8 copula (180 degrees; “survival BB8”) 23 = rotated Clayton copula (90 degrees) 24 = rotated Gumbel copula (90 degrees) 26 = rotated Joe copula (90 degrees) 27 = rotated BB1 copula (90 degrees) 28 = rotated BB6 copula (90 degrees) 29 = rotated BB7 copula (90 degrees) 30 = rotated BB8 copula (90 degrees) 33 = rotated Clayton copula (270 degrees) 34 = rotated Gumbel copula (270 degrees) 36 = rotated Joe copula (270 degrees) 37 = rotated BB1 copula (270 degrees) 38 = rotated BB6 copula (270 degrees) 39 = rotated BB7 copula (270 degrees) 40 = rotated BB8 copula (270 degrees)
一个整数，定义二元Copula的家庭： 0独立系词参考1=高斯系词参考的2学生t Copula函数（T-Copula函数）参考3=克莱顿系词参考4= Gumbel分布Copula的参考5=弗兰克·系词参考6=乔系词参考7= BB1 Copula的参考8= BB6 Copula的参考9= BB7系词参考10= BB8系词参考13 =旋转克莱顿系词（180度参考“生存克莱顿”）14=旋转（180度“生存冈贝尔”）Gumbel分布Copula的参考16=旋转乔系词（180度“生存乔” ）参考17=旋转BB1 Copula函数（180度;“BB1生存”）参考18=旋转BB6 Copula函数（180度“生存BB6”）参考所述> =旋转BB7系词（180度“生存BB7”）参考19=旋转BB8系词（180度“生存BB8”）参考20=旋转克莱顿系词（90度）参考23=系词（90度）旋转冈贝尔参考24=旋转乔系词（90度）参考26=旋转BB1 Copula函数（ 90度）参考27=旋转BB6系词（90度）参考28=旋转BB7系词（90度）参考29=旋转BB8系词（90度）参考30=系词（270度）旋转克莱顿参考33=系词（270度）旋转冈贝尔参考34=旋转乔系词（270度） 36=旋转BB1 Copula函数（270度）参考37=旋转BB6 Copula函数（270度）参考38=旋转BB7系词（270度）参考39=旋转BB8系词（270度）

参数：method
Character indicating the estimation method: either maximum likelihood estimation (method = "mle"; default) or inversion of Kendall's tau (method = "itau"). For method = "itau" only one parameter bivariate copula families can be used (family = 1,3,4,5,6,13,14,16,23,24,26,33,34 or 36).
字符显示的估算方法：无论是最大似然估计（method = "mle";默认）或反转Kendall的tau（method = "itau"）。 对于method = "itau"只有一个参数可用于二元Copula的家庭（family = 1,3,4,5,6,13,14,16,23,24,26,33,34或36）。

参数：se
Logical; whether standard error(s) of parameter estimates is/are estimated (default: se = FALSE).
逻辑;，是否参数估计值的标准误差（S）/预计（默认：se = FALSE）。

参数：max.df
Numeric; upper bound for the estimation of the degrees of freedom parameter of the t-copula (default: max.df = 30).
数字;上界估计的程度自由的t-Copula函数的参数（默认值：max.df = 30）。

参数：max.BB
List; upper bounds for the estimation of the two parameters (in absolute values) of the BB1, BB6, BB7 and BB8 copulas (default: max.BB = list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1))).
名单;（绝对值），BB1，BB6，BB7和BB8 Copula函数的两个参数的估计上限为参考（默认：max.BB = list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1))）。

Details

详细信息----------Details----------

If method = "itau", the function computes the empirical Kendall's tau of the given copula data and exploits the one-to-one relationship of copula parameter and Kendall's tau which is available for many one parameter bivariate copula families (see BiCopPar2Tau and BiCopTau2Par). The inversion of Kendall's tau is however not available for all bivariate copula families (see above). If a two parameter copula family is chosen and method = "itau", a warning message is returned and the MLE is calculated.
如果method = "itau"，函数计算给定的Copula的数据和经验Kendall的tau利用Copula的参数和Kendall的tau一个一对一的关系，这是多一个参数二元Copula的家庭（见BiCopPar2Tau 和BiCopTau2Par“）。反转Kendall的tau，但并不适用于所有的二元Copula的家庭（见上文）。如果两个参数Copula的家庭选择和method = "itau"，一个警告消息，则返回和极大似然估计的计算方法。

For method = "mle" copula parameters are estimated by maximum likelihood using starting values obtained by method = "itau". If no starting values are available by inversion of Kendall's tau, starting values have to be provided given expert knowledge and the boundaries max.df and max.BB respectively. Note: The MLE is performed via numerical maximazation using the L_BFGS-B method. For the Gaussian, the t- and the one-parametric Archimedean copulas we can use the gradients, but for the BB copulas we have to use finite differences for the L_BFGS-B method.
对于method = "mle" Copula函数参数估计的最大似然开始得到method = "itau"值。如果没有初始值是反转Kendall的tau，初始值必须提供的专业知识和的边界max.df和max.BB分别。注：MLE通过数值的最大化提供使用L_BFGS-B的方法。为高斯，T-和一个参数阿基米德Copula函数，我们可以使用的梯度，但BB Copula函数，我们必须使用有限L_BFGS-B方法的差异。

A warning message is returned if the estimate of the degrees of freedom parameter of the t-copula is larger than max.df. For high degrees of freedom the t-copula is almost indistinguishable from the Gaussian and it is advised to use the Gaussian copula in this case. As a rule of thumb max.df = 30 typically is a good choice. Moreover, standard errors of the degrees of freedom parameter estimate cannot be estimated in this case.
一条警告消息，返回，如果程度的自由的t-Copula函数的参数估计是大于max.df。高自由度的t-Copula函数的高斯几乎是没有什么区别的，它是在这种情况下，建议使用高斯Copula的。作为一个经验法则max.df = 30通常是一个不错的选择。此外，不能被估计标准误差程度的自由参数估计，在这种情况下。

值----------Value----------

参数：par, par2
Estimated copula parameter(s).
估计Copula函数的参数（S）。

参数：se,se2
Standard error(s) of the parameter estimate(s) (if se = TRUE).
标准误差（S）的参数估计值（S）（se = TRUE）。

（作者）----------Author(s)----------

Ulf Schepsmeier, Eike Brechmann, Jakob Stoeber, Carlos Almeida

参考文献----------References----------

Multivariate Models and Dependence Concepts. Chapman and Hall, London.

参见----------See Also----------

BiCopPar2Tau, BiCopTau2Par RVineSeqEst, BiCopSelect
BiCopPar2Tau，BiCopTau2ParRVineSeqEst，BiCopSelect

实例----------Examples----------

## Example 1: bivariate Gaussian copula[例1：二元高斯Copula函数]
dat = BiCopSim(500,1,0.7)
u1 = dat[,1]
v1 = dat[,2]

# empirical Kendall's tau[经验Kendall的tau]
tau1 = cor(u1,v1,method="kendall")

# inversion of empirical Kendall's tau [反转的经验Kendall的tau]
BiCopTau2Par(1,tau1)
BiCopEst(u1,v1,family=1,method="itau")$par

# maximum likelihood estimate for comparison[最大似然估计的比较]
BiCopEst(u1,v1,family=1,method="mle")$par

## Example 2: bivariate Clayton and survival Gumbel copulas[例2：二元Clayton和Gumbel分布Copula函数求生存]
# simulate from a Clayton copula[模拟从克莱顿系词]
dat = BiCopSim(500,3,2.5)
u2 = dat[,1]
v2 = dat[,2]

# empirical Kendall's tau[经验Kendall的tau]
tau2 = cor(u2,v2,method="kendall")

# inversion of empirical Kendall's tau for the Clayton copula[“克莱顿Copula的经验Kendall的tau反转]
BiCopTau2Par(3,tau2)
BiCopEst(u2,v2,family=3,method="itau",se=TRUE)

# inversion of empirical Kendall's tau for the survival Gumbel copula[冈贝尔Copula的生存经验Kendall的tau反转]
BiCopTau2Par(14,tau2)
BiCopEst(u2,v2,family=14,method="itau",se=TRUE)

# maximum likelihood estimates for comparison[最大似然估计进行比较]
BiCopEst(u2,v2,family=3,method="mle",se=TRUE)
BiCopEst(u2,v2,family=14,method="mle",se=TRUE)

转载请注明:出自生物统计家园网(http://www.biostatistic.net)。

注：
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