| Type: | Package |
| Title: | A Fast Implementation of Distance Covariance |
| Version: | 0.1.1 |
| Author: | Hang Weiqiang <e0010758@u.nus.edu> |
| Maintainer: | Hang Weiqiang <e0010758@u.nus.edu> |
| Description: | Efficient methods for computing distance covariance and relevant statistics. See Székely et al.(2007) <doi:10.1214/009053607000000505>; Székely and Rizzo (2013) <doi:10.1016/j.jmva.2013.02.012>; Székely and Rizzo (2014) <doi:10.1214/14-AOS1255>; Huo and Székely (2016) <doi:10.1080/00401706.2015.1054435>. |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| LazyData: | true |
| Imports: | Rcpp |
| LinkingTo: | Rcpp, RcppArmadillo |
| RoxygenNote: | 6.1.1 |
| NeedsCompilation: | yes |
| Packaged: | 2020-06-25 19:00:18 UTC; weiqianghang |
| Repository: | CRAN |
| Date/Publication: | 2020-06-25 21:30:02 UTC |
Centering method This method implements the double centering and U-centering during computing distance covariance.
Description
Centering method This method implements the double centering and U-centering during computing distance covariance.
Usage
centering(D, type = c("V", "U"))
centering_from_data(x, type = c("V", "U"))
Arguments
D |
the pairwise distance matrix |
type |
"V" or "U". "V" for double centering. "U" for U-centering. |
x |
the matrix of x |
Examples
x = matrix(rnorm(200),100,2)
D = as.matrix(dist(x))
A = centering(D,'U')
A = centering_from_data(x)
Permutation test of distance correlation and partial distance correlation
Description
Simple independence test based on data permutation using distance correlation and partial distance correlation.
Usage
dcor.test(x, y, R = 500, type = c("V", "U"))
pdcor.test(x, y, z, R = 500, type = c("U", "V"))
Arguments
x |
the data of x |
y |
the data of y |
R |
the number of replicates |
type |
"U" or "V" |
z |
the data of controlling variables. Given z, pdcor between x and y is calculated. |
Examples
n = 200
z = rnorm(n)
x = rnorm(n)*z
y = rnorm(n)*z
res1 = dcor.test(x,y,R=500)
res2 = pdcor.test(x,y,z,R=500)
Distance correlation T-test It uses the result of U-statistic distance correlation to test independence for high dimensional data
Description
Distance correlation T-test It uses the result of U-statistic distance correlation to test independence for high dimensional data
Usage
dcor.ttest(x, y)
Arguments
x |
data of x |
y |
data of y |
Examples
n = 200
x = rnorm(n)
y = rnorm(n)
res = dcor.ttest(x,y)
Distance covariance
Description
This method implements the method to compute the value of distance covariance proposed by Székely et al.(2007) and Székely and Rizzo(2013) by Armadillo library. For distance covariance between two one dimensional variables, the fast algorithm proposed by Huo and Székely(2016) is used.
Usage
dcov(x, y, type = c("V", "U"))
dcor(x, y, type = c("V", "U"))
Arguments
x |
the matrix of x |
y |
the matrix of y |
type |
"V" or "U", for V- or U-statistics of distance covariance or correlation. The default value is "V". |
Note
Note that the result of dcov(x,y,"V") and dcor(x,y,"V")
is same with the result of energy::dcov(x,y)^2 and energy::dcor(x,y)^2.
The result of dcov(x,y,'U') and dcor(x,y,'U') is same with
the result of energy::dcovU(x,y) and energy::bcdcor(x,y).
References
Székely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007). Measuring and testing dependence by correlation of distances. The annals of statistics, 35(6), 2769-2794.
Székely, G. J., & Rizzo, M. L. (2013). The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis, 117, 193-213.
Huo, X., & Székely, G. J. (2016). Fast computing for distance covariance. Technometrics, 58(4), 435-447.
See Also
dcov2d
Examples
x = matrix(rnorm(200),100,2)
y = matrix(rnorm(200),100,2)
dcov(x,y)
dcor(x,y)
Fast distance covariance for two bivariate variables
Description
This method implements the fast algorithm proposed by Huo and Székely. The
result of dcov2d and dcor2d is same with the result of
energy::dcov2d and energy::dcor2d
Usage
dcov2d(x, y, type = c("V", "U"))
dcor2d(x, y, type = c("V", "U"))
Arguments
x |
the vector of x |
y |
the vector of y |
type |
"V" or "U", for V- or U-statistics of distance covariance or correlation. The default value is "V". |
References
Székely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007). Measuring and testing dependence by correlation of distances. The annals of statistics, 35(6), 2769-2794.
Székely, G. J., & Rizzo, M. L. (2013). The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis, 117, 193-213.
Huo, X., & Székely, G. J. (2016). Fast computing for distance covariance. Technometrics, 58(4), 435-447.
Examples
x = rnorm(200)
y = rnorm(200)
dcov2d(x,y)
dcor2d(x,y)
Marginal distance covariance This function implements the method of calculating distance covariance between y and each column in x
Description
Marginal distance covariance This function implements the method of calculating distance covariance between y and each column in x
Usage
mdcov(y, x, type = c("V", "U"))
mdcor(y, x, type = c("V", "U"))
Arguments
y |
the matrix of y |
x |
the matrix of x, distance covariance is calculated for each variable in x with y. |
type |
"V" or "U", for V- or U-statistics of distance covariance or correlation. The default value is "V". |
Examples
n = 200; p = 10
y = matrix(rnorm(n*2),n,2)
x = matrix(rnorm(n*p),n,p)
res1 = mdcov(y,x)
res2 = numeric(p)
for(j in 1:p){res2[j] = dcov::dcov(y,x[,j])}
# res1 is same with res2
res1 - res2
res3 = mdcor(y,x)
res4 = numeric(p)
for(j in 1:p){res4[j] = dcov::dcor(y,x[,j])}
# res3 is same with res4
res3-res4
Projection covariance between two random vectors This function implements the projection correlation in Zhu et al.(2017)
Description
Projection covariance between two random vectors This function implements the projection correlation in Zhu et al.(2017)
Usage
pcov(x, y)
Arguments
x |
the matrix of x |
y |
the matrix of y |
References
Zhu, L., Xu, K., Li, R., & Zhong, W. (2017). Projection correlation between two random vectors. Biometrika, 104(4), 829-843.
Examples
x = matrix(rnorm(200),100,2)
y = matrix(rnorm(200),100,2)
pcov(x,y)
Partial distance covariance
Description
This method implements the method to compute the value of partial distance covariance proposed by Székely and Rizzo, 2014.
Usage
pdcov(x, y, z, type = c("U", "V"))
pdcor(x, y, z, type = c("U", "V"))
Arguments
x |
the matrix of x |
y |
the matrix of y |
z |
the matrix of z. Given the value of z, pdcov or pdcor between x and y is calcuated. |
type |
"V" or "U", for V- or U-statistics of partial distance covariance or correlation. The default value is "U". |
References
Székely, G. J., & Rizzo, M. L. (2014). Partial distance correlation with methods for dissimilarities. The Annals of Statistics, 42(6), 2382-2412.
Examples
z = matrix(rnorm(400),200,2)
x = matrix(rnorm(400),200,2)*z
y = matrix(rnorm(400),200,2)*z
pdcov(x,y,z)
pdcor(x,y,z)