lcor.ci: Confidence intervals for the Lancaster correlation...

In lancor: Statistical Inference via Lancaster Correlation

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.

Details

Computes asymptotic and bootstrap-based confidence intervals for the (linear) Lancaster correlation coefficient \rho_L (\rho_{L,1}). For more details see lcor.

Asymptotic confidence intervals are derived under two cases (analogously for \rho_{L}; see Holzmann and Klar (2024)):

Case 1: If |\rho_{L1}|\neq|\rho_{L2}|, the 1-\alpha asymptotic interval is

\left[ \max\{\hat\rho_{L,1} - z_{1-\alpha/2}\,s/\sqrt{n}, 0\},\ \min\{\hat\rho_{L,1} + z_{1-\alpha/2}\,s/\sqrt{n}, 1\} \right],

where z_{1-\alpha/2} is the standard normal quantile and s is an estimator of the corresponding standard deviation.

Case 2: If |\rho_{L1}|=|\rho_{L2}|=a>0, let \tau denote the correlation between the two components and let q_{1-\alpha/2} be the 1-\alpha/2 quantile of the asymptotic distribution of \sqrt{n}(\hat\rho_{L,1} - a). A conservative asymptotic interval is

\left[ \max\{\hat\rho_{L,1} - q_{1-\alpha/2}/\sqrt{n}, 0\},\ \min\{\hat\rho_{L,1} + z_{1-\alpha/2}\,s/\sqrt{n}, 1\} \right].

Additionally, bootstrap-based intervals can be obtained by resampling and estimating the covariance matrix of the rank or linear correlation components.

Value

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". \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1111/sjos.12733")}

See Also

lcor, lcor.comp, lcor.test

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")

lancor documentation built on Aug. 22, 2025, 9:16 a.m.