BiCopSelect(VineCopula)
BiCopSelect()所属R语言包：VineCopula
Selection and maximum likelihood estimation of bivariate copula families
选择和最大似然估计二元Copula的家庭的
译者：生物统计家园网 机器人LoveR
描述----------Description----------
This function selects an appropriate bivariate copula family for given bivariate copula data using one of a range of methods. The corresponding parameter estimates are obtained by maximum likelihood estimation.
此功能选择合适的二元Copula的家庭，对于给定的二元Copula的数据使用范围的方法之一。相应的参数估计，获得了最大似然估计。
用法----------Usage----------
BiCopSelect(u1, u2, familyset=NA, selectioncrit="AIC",
indeptest=FALSE, level=0.05)
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：familyset
Vector of bivariate copula families to select from (the independence copula MUST NOT be specified in this vector, otherwise it will be selected). The vector has to include at least one bivariate copula family that allows for positive and one that allows for negative dependence. If familyset = NA (default), selection among all possible families is performed. Coding of bivariate copula families: <br> 1 = Gaussian copula <br> 2 = Student t copula (t-copula) <br> 3 = Clayton copula <br> 4 = Gumbel copula <br> 5 = Frank copula <br> 6 = Joe copula <br> 7 = BB1 copula <br> 8 = BB6 copula <br> 9 = BB7 copula <br> 10 = BB8 copula <br> 13 = rotated Clayton copula (180 degrees; “survival Clayton”) <br> 14 = rotated Gumbel copula (180 degrees; “survival Gumbel”) <br> 16 = rotated Joe copula (180 degrees; “survival Joe”) <br> 17 = rotated BB1 copula (180 degrees; “survival BB1”)<br> 18 = rotated BB6 copula (180 degrees; “survival BB6”)<br> 19 = rotated BB7 copula (180 degrees; “survival BB7”)<br> 20 = rotated BB8 copula (180 degrees; “survival BB8”)<br> 23 = rotated Clayton copula (90 degrees) <br> 24 = rotated Gumbel copula (90 degrees) <br> 26 = rotated Joe copula (90 degrees) <br> 27 = rotated BB1 copula (90 degrees) <br> 28 = rotated BB6 copula (90 degrees) <br> 29 = rotated BB7 copula (90 degrees) <br> 30 = rotated BB8 copula (90 degrees) <br> 33 = rotated Clayton copula (270 degrees) <br> 34 = rotated Gumbel copula (270 degrees) <br> 36 = rotated Joe copula (270 degrees) <br> 37 = rotated BB1 copula (270 degrees) <br> 38 = rotated BB6 copula (270 degrees) <br> 39 = rotated BB7 copula (270 degrees) <br> 40 = rotated BB8 copula (270 degrees)
向量二元Copula的家庭的选择（独立Copula函数，不得指定在此向量，否则会被选中）。该向量具有包括至少一个二元系词家庭，使正极和一个允许负依赖性。如果familyset = NA（默认），在所有可能的家庭进行选择。编码二元Copula的家庭：<BR>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Copula的参考< x> = Gumbel分布Copula的参考4=弗兰克·系词参考5=乔系词参考6= BB1 Copula的参考7= BB6 Copula函数参考8= BB7系词参考9= BB8系词参考10=旋转克莱顿系词（180度“生存克莱顿”），参考<X > =旋转（180度“生存冈贝尔”）Gumbel分布Copula的参考13=旋转乔系词（180度;“生存乔”）参考14=旋转BB1 Copula函数（180度;“BB1生存”）参考16=旋转（180度“生存BB6”）BB6 Copula的参考17=旋转BB7系词（180度;生存BB7“）参考18=旋转（180度”生存BB8“）BB8系词参考19=旋转克莱顿系词（90度）参考20旋转冈贝尔系词（90度）参考23=旋转乔系词（90度）参考24=旋转BB1 Copula函数（90度）参考26=旋转BB6 Copula函数（90度）参考27=旋转BB7系词（90度）参考28=旋转BB8系词（90度）参考29=旋转克莱顿系词（270度）参考30=系词（270度）旋转冈贝尔参考33=旋转乔系词（270度）参考34=旋转BB1 Copula函数（270度）参考36=旋转BB6 Copula函数（270度）参考37=旋转BB7系词（270度）参考38=旋转BB8系词（270度）
参数：selectioncrit
Character indicating the criterion for bivariate copula selection. Possible choices: selectioncrit = "AIC" (default) or "BIC".
字符，指示二元Copula函数选择的标准。可能的选择：selectioncrit = "AIC"（默认）或"BIC"。
参数：indeptest
Logical; whether a hypothesis test for the independence of u1 and u2 is performed before bivariate copula selection (default: indeptest = FALSE; cp. BiCopIndTest). The independence copula is chosen if the null hypothesis of independence cannot be rejected.
逻辑，无论的假设检验的独立性u1和u2之前进行二元Copula函数的选择（默认：indeptest = FALSE; CP。BiCopIndTest）。独立Copula的选择，如果独立的零假设不能被拒绝。
参数：level
Numeric; significance level of the independence test (default: level = 0.05).
数字的独立性检验的显着性水平（默认：level = 0.05）。
Details
详细信息----------Details----------
Copulas can be selected according to the Akaike and Bayesian Information Criteria (AIC and BIC, respectively). First all available copulas are fitted using maximum likelihood estimation. Then the criteria are computed for all available copula families (e.g., if u1 and u2 are negatively dependent, Clayton, Gumbel, Joe, BB1, BB6, BB7 and BB8 and their survival copulas are not considered) and the family with the minimum value is chosen. For observations u_{i,j}, i=1,...,N,\ j=1,2, the AIC of a bivariate copula family c with parameter(s) \boldsymbol{θ} is defined as
可根据Copula函数的Akaike贝叶斯信息标准（AIC及BIC，分别）。首先安装使用所有可用的Copula函数的极大似然估计。的标准计算所有可用的Copula的家庭（例如，如果u1和u2是负相关，克莱顿，耿贝尔，乔，BB1，BB6，BB7，BB8和他们的生存Copula函数不考虑）和家庭用的最小的值被选择。的观测u_{i,j}, i=1,...,N,\ j=1,2,AIC的二元Copula的家庭c参数（S）\boldsymbol{θ}被定义为
where k=1 for one parameter copulas and k=2 for the two parameter t-, BB1, BB6, BB7 and BB8 copulas. Similarly, the BIC is given by
k=1一个参数Copula函数和k=2T-BB1，BB6，BB7和BB8 Copula函数两个参数。同样地，由下式给出的BIC
Evidently, if the BIC is chosen, the penalty for two parameter families is stronger than when using the AIC.
很显然，如果选择的BIC，处罚的两个参数家庭比使用AIC时。
Additionally a test for independence can be performed beforehand.
此外可以事先进行独立测试。
值----------Value----------
参数：family
The selected bivariate copula family.
选定的二元Copula的家庭。
参数：par, par2
The estimated bivariate copula parameter(s).
估计二元Copula函数的参数（S）。
参数：p.value.indeptest
P-value of the independence test if performed.
P-值，如果进行的独立测试。
注意----------Note----------
When the bivariate t-copula is considered and the degrees of freedom are estimated to be larger than 30, then the bivariate Gaussian copula is taken into account instead. Similarly, when BB1 (Clayton-Gumbel), BB6 (Joe-Gumbel), BB7 (Joe-Clayton) or BB8 (Joe-Frank) copulas are considered and the parameters are estimated to be very close to one of their boundary cases, the respective one parameter copula is taken into account instead.
当二元T-Copula的考虑和估计的自由度大于30，那么二元高斯Copula的，而不是考虑。同样，当被认为是BB1（克莱顿 - 耿贝尔），，BB6（乔 - 耿贝尔），BB7（乔·克莱顿）或BB8（乔 - 弗兰克）Copula函数的参数估计是非常靠近两国边界的情况下，相应的一个参数Copula的考虑。
（作者）----------Author(s)----------
Eike Brechmann, Jeffrey Dissmann
参考文献----------References----------
Information theory and an extension of the maximum likelihood principle. In B. N. Petrov and F. Csaki (Eds.), Proceedings of the Second International Symposium on Information Theory Budapest, Akademiai Kiado, pp. 267-281.
Truncated and simplified regular vines and their applications. Diploma thesis, Technische Universitaet Muenchen.<br> http://mediatum.ub.tum.de/?id=1079285.
Estimation and model selection of copulas with an application to exchange rates. METEOR research memorandum 07/056, Maastricht University.
Estimating the dimension of a model. Annals of Statistics 6 (2), 461-464.
参见----------See Also----------
RVineStructureSelect, RVineCopSelect, BiCopIndTest
RVineStructureSelect，RVineCopSelect，BiCopIndTest
实例----------Examples----------
## Example 1: Gaussian copula with large dependence parameter[例1：高斯系词与大量依赖参数]
par1 = 0.7
fam1 = 1
dat1 = BiCopSim(500,fam1,par1)
# select the bivariate copula family and estimate the parameter(s)[选择二元Copula的家庭的和估计的参数（S）]
cop1 = BiCopSelect(dat1[,1],dat1[,2],familyset=c(1:10),indeptest=FALSE,
level=0.05)
cop1$family
cop1$par
cop1$par2
## Example 2: Gaussian copula with small dependence parameter[例2：高斯Copula的依赖性小参数]
par2 = 0.01
fam2 = 1
dat2 = BiCopSim(500,fam2,par2)
# select the bivariate copula family and estimate the parameter(s)[选择二元Copula的家庭的和估计的参数（S）]
cop2 = BiCopSelect(dat2[,1],dat2[,2],familyset=c(1:10),indeptest=TRUE,
level=0.05)
cop2$family
cop2$par
cop2$par2
## Example 3: empirical data[例3：经验数据]
data(daxreturns)
cop3 = BiCopSelect(daxreturns[,1],daxreturns[,4],
familyset=c(1:10,13,14,16,23,24,26))
cop3$family
cop3$par
cop3$par2
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。
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发表于 2012-10-1 16:10:26
