SCSrank {MCPAN}

Compute a rectangular simultaneous confidence set from a sample of a joint empirical distribution.

Description

Given a large sample of N values from an M dimensional joint empirical distribution, the rank based method of Besag et al. (1995) is used to compute a rectangular M-dimensional 'confidence' set that includes N*conf.level values of the sample.

Usage

SCSrank(x, conf.level = 0.95, alternative = "two.sided", ...)

Arguments

x

an N x M matrix containg N sampled values of the M dimensional distribution of interest

conf.level

the simultaneous confidence level, a single numeric value between 0 and 1, defaults to 0.95 for simultaneous 95 percent sets

alternative

a single character string related to hypotheses testing, "two.sided" invokes two-sided confidence sets, "less" invokes sets with upper limits only and "greater" invokes sets with lower limits only,

...

currently ignored

Value

an Mx2 (alternative="two.sided") matrix containing the lower and upper confidence limist for the M dimensions, in case of alternative="less", alternative="greater" the lower and upper bounds are replaced by -Inf and Inf, respectively.

Author(s)

Frank Schaarschmidt

References

Besag J, Green P, Higdon D, Mengersen K (1995). Bayesian Computation and Stochastic Systems. Statistical Science 10, 3-66. Mandel M, Betensky RA. Simultaneous confidence intervals based on the percentile bootstrap approach. Computational Statistics and Data Analysis 2008; 52(4): 2158-2165.

Examples

x <- cbind(rnorm(1000,1,2), rnorm(1000,0,2), rnorm(1000,0,0.5), rnorm(1000,2,1))
dim(x)
cm <- rbind(c(-1,1,0,0), c(-1,0,1,0), c(-1, 0,0,1))
xd <- t(apply(x, 1, function(x){crossprod(t(cm), matrix(x))}))
pairs(xd)

SCSrank(xd, conf.level=0.9)