R: Compute a rectangular simultaneous confidence set from a...

SCSrank {MCPAN} | R Documentation

## 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)

[Package MCPAN version 1.1-21 Index]