, Hajo Holzmann [aut]| Title: | Statistical Inference via Lancaster Correlation |
|---|---|
| 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. |
| Authors: | Bernhard Klar [aut, cre]
, Hajo Holzmann [aut] |
| Maintainer: | Bernhard Klar <[email protected]> |
| License: | GPL-2 |
| Version: | 0.1.2 |
| Built: | 2025-01-31 04:09:15 UTC |
| Source: | https://github.com/cran/lancor |
Performs a permutation test of independence using ace in package acepack. ace stands for alternating conditional expectations.
ace.test(x, y = NULL, nperm = 999)ace.test(x, y = NULL, nperm = 999)
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. |
A list containing the following components:
ace |
the value of the test statistic. |
pval |
the p-value of the test. |
Hajo Holzmann, Bernhard Klar
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
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)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)
Computes the Lancaster correlation coefficient.
lcor(x, y = NULL, type = c("rank", "linear"))lcor(x, y = NULL, type = c("rank", "linear"))
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. |
lcor returns the sample Lancaster correlation.
Hajo Holzmann, Bernhard Klar
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
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")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")
Computes confidence intervals for the Lancaster correlation coefficient. Lancaster correlation is a bivariate measures of dependence.
lcor.ci(x, y = NULL, conf.level = 0.95, type = c("rank", "linear"), con = TRUE, R = 1000, method = c("plugin", "boot", "pretest"))lcor.ci(x, y = NULL, conf.level = 0.95, type = c("rank", "linear"), con = TRUE, R = 1000, method = c("plugin", "boot", "pretest"))
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. |
lcor.ci returns a vector containing the lower and upper limits of the confidence interval.
Hajo Holzmann, Bernhard Klar
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
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")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")
Computes the Lancaster correlation coefficient and its components.
lcor.comp(x, y = NULL, type = c("rank", "linear"), plot = FALSE)lcor.comp(x, y = NULL, type = c("rank", "linear"), plot = FALSE)
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. |
lcor.comp returns a vector containing the two components rho1 and rho2 and the sample Lancaster correlation.
Hajo Holzmann, Bernhard Klar
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
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)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 of bivariate independence. Lancaster correlation is a bivariate measures of dependence.
lcor.test(x, y = NULL, type = c("rank", "linear"), nperm = 999, method = c("permutation", "asymptotic", "symmetric"))lcor.test(x, y = NULL, type = c("rank", "linear"), nperm = 999, method = c("permutation", "asymptotic", "symmetric"))
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. |
A list containing the following components:
lcor |
the value of the test statistic. |
pval |
the p-value of the test. |
Hajo Holzmann, Bernhard Klar
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
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")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")
Estimate of covariance matrix of the two components of Lancaster correlation. Lancaster correlation is a bivariate measures of dependence.
Sigma.est(xx)Sigma.est(xx)
xx |
a matrix or data frame with two columns. |
Sigma.est returns the estimated covariance matrix.
Hajo Holzmann, Bernhard Klar
Holzmann, Klar (2024) Lancester correlation - a new dependence measure linked to maximum correlation. arXiv:2303.17872
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)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)