centcosums: Multivariate centered sums; join and unjoined.
In fromo: Fast Robust Moments

Description Usage Arguments Value Note Author(s) References See Also Examples

Compute, join, or unjoin multivariate centered (co-) sums.

cent_cosums(v, max_order = 2L, na_omit = FALSE)

cent_comoments(v, max_order = 2L, used_df = 0L, na_omit = FALSE)

join_cent_cosums(ret1, ret2)

unjoin_cent_cosums(ret3, ret2)

`v`	an m by n matrix, each row an independent observation of some n variate variable.
`max_order`	the maximum order of cosum to compute. For now this can only be 2; in the future higher order cosums should be possible.
`na_omit`	a boolean; if `TRUE`, then only rows of `v` with complete observations will be used.
`used_df`	the number of degrees of freedom consumed, used in the denominator of the centered moments computation. These are subtracted from the number of observations.
`ret1`	a multdimensional array as output by `cent_cosums`.
`ret2`	a multdimensional array as output by `cent_cosums`.
`ret3`	a multdimensional array as output by `cent_cosums`.

a multidimensional arry of dimension max_order, each side of length 1+n. For the case currently implemented where max_order must be 2, the output is a symmetric matrix, where the element in the 1,1 position is the count of complete) rows of v, the 2:(n+1),1 column is the mean, and the 2:(n+1),2:(n+1) is the co sums matrix, which is the covariance up to scaling by the count. cent_comoments performs this normalization for you.

The moment computations provided by fromo are numerically robust, but will often not provide the same results as the 'standard' implementations, due to differences in roundoff. We make every attempt to balance speed and robustness. User assumes all risk from using the fromo package.

Steven E. Pav shabbychef@gmail.com

Terriberry, T. "Computing Higher-Order Moments Online." http://people.xiph.org/~tterribe/notes/homs.html

J. Bennett, et. al., "Numerically Stable, Single-Pass, Parallel Statistics Algorithms," Proceedings of IEEE International Conference on Cluster Computing, 2009. https://www.semanticscholar.org/paper/Numerically-stable-single-pass-parallel-statistics-Bennett-Grout/a83ed72a5ba86622d5eb6395299b46d51c901265

Cook, J. D. "Accurately computing running variance." http://www.johndcook.com/standard_deviation.html

Cook, J. D. "Comparing three methods of computing standard deviation." http://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation

cent_sums

 set.seed(1234)
 x1 <- matrix(rnorm(1e3*5,mean=1),ncol=5)
 x2 <- matrix(rnorm(1e3*5,mean=1),ncol=5)
 max_ord <- 2L
 rs1 <- cent_cosums(x1,max_ord)
 rs2 <- cent_cosums(x2,max_ord)
 rs3 <- cent_cosums(rbind(x1,x2),max_ord)
 rs3alt <- join_cent_cosums(rs1,rs2)
 stopifnot(max(abs(rs3 - rs3alt)) < 1e-7)
 rs1alt <- unjoin_cent_cosums(rs3,rs2)
 rs2alt <- unjoin_cent_cosums(rs3,rs1)
 stopifnot(max(abs(rs1 - rs1alt)) < 1e-7)
 stopifnot(max(abs(rs2 - rs2alt)) < 1e-7)