nPM | R Documentation |
Given a multivariate data sample, the function returns an estimate of a product of joint cumulants with fixed orders.
nPM( v = NULL, V = NULL)
v |
list of integer vectors |
V |
vector of a multivariate data sample |
Multivariate polykays or multivariate generalized k-statistics are unbiased estimators of
joint cumulant products with minimum variance. See the referred papers to read more about these estimators. Multivariate polykays
are usually expressed in terms of power sum symmetric polynomials in the random vectors of the sample.
Thus, for the input multivariate sample data
, running
nPM( list( c(r1, s1, ...), c(r1, s2, ...),.. ), data)
returns an estimate of the product
k[r1, s1,....]*k[r2, s2, ...]*...
where k[r1, s1,....], k[r2, s2, ...], ...
are
the joint cumulants of the population distribution.
float |
the estimate of the multivariate polykay |
The size of each data vector must be equal to the length of the vector passed trough the first input variable. The vectors in the list must have the same length.
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
nPolyk
,
nKS
,
nKM
,
nPS
# 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 product k[2,1]*k[1,0], where k[2,1] and k[1,0] are the # cross-correlation of order (2,1) and the marginal mean of the population distribution # respectively nPM( list( c(2,1), c(1,0) ), 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 product k[2,0,1]*k[1,1,0], where k[2,0,1] and k[1,1,0] # are joint cumulants of the population distribution nPM( list( c(2,0,1), c(1,1,0) ), data2)
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