Version: 1.1
Date: 2024-06-02
Title: Jackknife Euclidean / Empirical Likelihood Inference for Spearman's Rho
Description: Functions for conducting jackknife Euclidean / empirical likelihood inference for Spearman's rho (de Carvalho and Marques (2012) <doi:10.1080/10920277.2012.10597644>).
Author: Miguel de Carvalho [aut, cre]
Depends: R (≥ 3.0.1)
Maintainer: Miguel de Carvalho <miguel.decarvalho@ed.ac.uk>
License: GPL (≥ 3)
Repository: CRAN
Imports: emplik, MASS
NeedsCompilation: no
Packaged: 2024-06-02 15:07:41 UTC; muad'dib
Date/Publication: 2024-06-02 15:20:02 UTC

Danish Fire Insurance Claims Database

Description

Danish Fire Insurance Claims Database includes 2167 industrial fire losses gathered from the Copenhagen Reinsurance Company over the period 1980–1990.

Usage

data(fire)

Format

A dataframe with 2167 observations on five variables. The object is of class data.frame.

Examples

data(fire)
attach(fire)
plot(building, contents, pch = 20, xlim = c(0,95), ylim = c(0,133),
     xlab = "Loss of Building", ylab = "Loss of Contents",
     main = "Danish Fire Insurance Claims")

Jackknife Euclidean / Empirical Likelihood Inference for Spearman's Correlation

Description

Computes jackknife Euclidean / empirical likelihood confidence intervals for Spearman's correlation.

Usage

spearmanCI(x, y, level = 0.95, method = "Euclidean", plot = FALSE)

Arguments

x

vector with data.

y

vector with data.

level

the confidence level required.

method

this must be one of the strings "Euclidean" or "empirical"; see references below for details.

plot

logical; if TRUE, it plots log-likelihood ratio function.

Author(s)

Miguel de Carvalho

References

de Carvalho, M. and Marques, F. J. (2012). Jackknife Euclidean likelihood-based inference for Spearman's rho. North American Actuarial Journal, 16, 487–492.

Wang, R., and Peng, L. (2011). Jackknife empirical likelihood intervals for Spearman’s rho. North American Actuarial Journal, 15, 475–486.

Examples

## Real data example
data(fire)
attach(fire)
spearmanCI(building, contents)

## The intervals in de Carvalho and Marques (2012, Section 3.2)
## differ slightly as they are based on the estimate 
## spearman <- function(x, y) {
##  n <- length(x)
##  F <- ecdf(x); G <- ecdf(y)
##  return(12 / n * sum((F(x) - 1 / 2) * (G(y) - 1 / 2)))  
## }

## Simulated data example
library(MASS)
pearson <- .7
Sigma <- matrix(c(1, pearson, pearson, 1), 2, 2)
xy <- mvrnorm(n = 1000, rep(0, 2), Sigma)
spearmanCI(xy[, 1], xy[, 2])
abline(v = 6 / pi * asin(pearson / 2), col = "grey", lty = 3)