MCPAN (version 1.1-22)

SCSrank: 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", ...)

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.

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

Author

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)