nKM | R Documentation |
Given a multivariate data sample, the function returns an estimate of a joint (or multivariate) cumulant with a fixed order.
nKM( v = NULL, V = NULL)
v |
vector of integers |
V |
vector of a multivariate data sample |
For a sample of i.i.d. random vectors, multivariate k-statistics are unbiased estimators of
the population joint cumulants with minimum variance and are expressed in terms of power sum symmetric polynomials
in the random vectors of the sample. See the referred papers to read more about these estimators.
Thus, for the input multivariate sample data
, running
nKM( c(r, s, ...), data)
with fixed order v=(r, s, ...)
returns an estimate of the joint cumulant
k[r, s, ...]
of the population distribution.
float |
the value of the multivariate k-statistics |
The size of each data vector must be equal to the length of the vector passed trough the first input variable.
Called by the master nPolyk
function in the kStatistics
package.
Elvira Di Nardo elvira.dinardo@unito.it,
Giuseppe Guarino giuseppe.guarino@rete.basilicata.it
E. Di Nardo, G. Guarino, D. Senato (2008) An unifying framework for k-statistics, polykays and their generalizations. Bernoulli. 14(2), 440-468. (download from https://arxiv.org/pdf/math/0607623.pdf)
E. Di Nardo, G. Guarino, D. Senato (2008) Symbolic computation of moments of sampling distributions. Comp. Stat. Data Analysis. 52(11), 4909-4922. (download from https://arxiv.org/abs/0806.0129)
E. Di Nardo, G. Guarino, D. Senato (2009) A new method for fast computing unbiased estimators of cumulants. Statistics and Computing, 19, 155-165. (download from https://arxiv.org/abs/0807.5008)
P. McCullagh, J. Kolassa (2009), Scholarpedia, 4(3):4699. http://www.scholarpedia.org/article/Cumulants
nKS
,
nPS
,
nPM
# Data assignment data1<-list(c(5.31,11.16),c(3.26,3.26),c(2.35,2.35),c(8.32,14.34),c(13.48,49.45), c(6.25,15.05),c(7.01,7.01),c(8.52,8.52),c(0.45,0.45),c(12.08,12.08),c(19.39,10.42)) # Return an estimate of the joint cumulant k[2,1] nKM(c(2,1),data1) # Data assignment data2<-list(c(5.31,11.16,4.23),c(3.26,3.26,4.10),c(2.35,2.35,2.27), c(4.31,10.16,6.45),c(3.1,2.3,3.2),c(3.20, 2.31, 7.3)) # Return an estimate of the joint cumulant k[2,2,2] nKM(c(2,2,2),data2) # Data assignment data3<-list(c(5.31,11.16,4.23,4.22),c(3.26,3.26,4.10,4.9),c(2.35,2.35,2.27,2.26), c(4.31,10.16,6.45,6.44),c(3.1,2.3,3.2,3.1),c(3.20, 2.31, 7.3,7.2)) # Return an estimate of the joint cumulant k[2,1,1,1] nKM(c(2,1,1,1),data3)
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