| Type: | Package |
| Title: | Statistical Inference via Lancaster Correlation |
| Version: | 0.1.2 |
| Description: | Implementation of the methods described in Holzmann, Klar (2024) <doi:10.48550/arXiv.2303.17872>. Lancaster correlation is a correlation coefficient which equals the absolute value of the Pearson correlation for the bivariate normal distribution, and is equal to or slightly less than the maximum correlation coefficient for a variety of bivariate distributions. Rank and moment-based estimators and corresponding confidence intervals are implemented, as well as independence tests based on these statistics. |
| Imports: | acepack, arrangements, boot, graphics, sn, stats |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.1 |
| Suggests: | testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | no |
| Packaged: | 2024-05-02 06:52:25 UTC; Klar |
| Author: | Bernhard Klar 
[aut, cre],
Hajo Holzmann [aut] |
| Maintainer: | Bernhard Klar <bernhard.klar@kit.edu> |
| Repository: | CRAN |
| Date/Publication: | 2024-05-02 15:22:42 UTC |
Covariance matrix of components of Lancaster correlation coefficient.
Description
Estimate of covariance matrix of the two components of Lancaster correlation. Lancaster correlation is a bivariate measures of dependence.
Usage
Sigma.est(xx)
Arguments
xx |
a matrix or data frame with two columns. |
Value
Sigma.est returns the estimated covariance matrix.
Author(s)
Hajo Holzmann, Bernhard Klar
References
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
See Also
Examples
Sigma <- matrix(c(1,0.1,0.1,1), ncol=2)
R <- chol(Sigma)
n <- 1000
x <- matrix(rnorm(n*2), n)
nu <- 8
y <- x / sqrt(rchisq(n, nu)/nu) #multivariate t
Sigma.est(y)
ACE permutation test of independence
Description
Performs a permutation test of independence using ace in package acepack. ace stands for alternating conditional expectations.
Usage
ace.test(x, y = NULL, nperm = 999)
Arguments
x |
a numeric vector, or a matrix or data frame with two columns. |
y |
NULL (default) or a vector with same length as x. |
nperm |
number of permutations. |
Value
A list containing the following components:
ace |
the value of the test statistic. |
pval |
the p-value of the test. |
Author(s)
Hajo Holzmann, Bernhard Klar
References
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
See Also
Examples
n <- 200
x <- matrix(rnorm(n*2), n)
nu <- 2
y <- x / sqrt(rchisq(n, nu)/nu) #multivariate t
cor.test(y[,1], y[,2], method = "spearman")
ace.test(y)
Lancaster correlation
Description
Computes the Lancaster correlation coefficient.
Usage
lcor(x, y = NULL, type = c("rank", "linear"))
Arguments
x |
a numeric vector, or a matrix or data frame with two columns. |
y |
NULL (default) or a vector with same length as x. |
type |
a character string indicating which lancaster correlation is to be computed. One of "rank" (default), or "linear": can be abbreviated. |
Value
lcor returns the sample Lancaster correlation.
Author(s)
Hajo Holzmann, Bernhard Klar
References
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
See Also
Examples
Sigma <- matrix(c(1,0.1,0.1,1), ncol=2)
R <- chol(Sigma)
n <- 1000
x <- matrix(rnorm(n*2), n)
lcor(x, type = "rank")
lcor(x, type = "linear")
x <- matrix(rnorm(n*2), n)
nu <- 2
y <- x / sqrt(rchisq(n, nu)/nu)
cor(y[,1], y[,2], method = "spearman")
lcor(y, type = "rank")
confidence intervals for the Lancaster correlation coefficient
Description
Computes confidence intervals for the Lancaster correlation coefficient. Lancaster correlation is a bivariate measures of dependence.
Usage
lcor.ci(x, y = NULL, conf.level = 0.95, type = c("rank", "linear"), con = TRUE,
R = 1000, method = c("plugin", "boot", "pretest"))
Arguments
x |
a numeric vector, or a matrix or data frame with two columns. |
y |
NULL (default) or a vector with same length as x. |
conf.level |
confidence level of the interval. |
type |
a character string indicating which lancaster correlation is to be computed. One of "rank" (default), or "linear": can be abbreviated. |
con |
logical; if TRUE (default), conservative asymptotic confidence intervals are computed. |
R |
number of bootstrap replications. |
method |
a character string indicating how the asymptotic covariance matrix is computed if type ="linear". One of "plugin" (default), "boot" or "symmetric": can be abbreviated. |
Value
lcor.ci returns a vector containing the lower and upper limits of the confidence interval.
Author(s)
Hajo Holzmann, Bernhard Klar
References
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
See Also
Examples
n <- 1000
x <- matrix(rnorm(n*2), n)
nu <- 2
y <- x / sqrt(rchisq(n, nu)/nu) # multivariate t
lcor(y, type = "rank")
lcor.ci(y, type = "rank")
Lancaster correlation and its components
Description
Computes the Lancaster correlation coefficient and its components.
Usage
lcor.comp(x, y = NULL, type = c("rank", "linear"), plot = FALSE)
Arguments
x |
a numeric vector, or a matrix or data frame with two columns. |
y |
NULL (default) or a vector with same length as x. |
type |
a character string indicating which lancaster correlation is to be computed. One of "rank" (default), or "linear": can be abbreviated. |
plot |
logical; if TRUE, scatterplots of the transformed x and y values and of their squares are drawn. |
Value
lcor.comp returns a vector containing the two components rho1 and rho2 and the sample Lancaster correlation.
Author(s)
Hajo Holzmann, Bernhard Klar
References
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
See Also
Examples
Sigma <- matrix(c(1,0.1,0.1,1), ncol=2)
R <- chol(Sigma)
n <- 1000
x <- matrix(rnorm(n*2), n)
nu <- 8
y <- x / sqrt(rchisq(n, nu)/nu) #multivariate t
cor(y[,1], y[,2])
lcor.comp(y, type = "linear")
x <- matrix(rnorm(n*2), n)
nu <- 2
y <- x / sqrt(rchisq(n, nu)/nu) #multivariate t
cor(y[,1], y[,2], method = "spearman")
lcor.comp(y, type = "rank", plot = TRUE)
Lancaster correlation test
Description
Lancaster correlation test of bivariate independence. Lancaster correlation is a bivariate measures of dependence.
Usage
lcor.test(x, y = NULL, type = c("rank", "linear"), nperm = 999,
method = c("permutation", "asymptotic", "symmetric"))
Arguments
x |
a numeric vector, or a matrix or data frame with two columns. |
y |
NULL (default) or a vector with same length as x. |
type |
a character string indicating which lancaster correlation is to be computed. One of "rank" (default), or "linear": can be abbreviated. |
nperm |
number of permutations. |
method |
a character string indicating how the p-value is computed if type ="linear". One of "permutation" (default), "asymptotic" or "symmetric": can be abbreviated. |
Value
A list containing the following components:
lcor |
the value of the test statistic. |
pval |
the p-value of the test. |
Author(s)
Hajo Holzmann, Bernhard Klar
References
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
See Also
Examples
n <- 200
x <- matrix(rnorm(n*2), n)
nu <- 2
y <- x / sqrt(rchisq(n, nu)/nu)
cor.test(y[,1], y[,2], method = "spearman")
lcor.test(y, type = "rank")