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

SCSrank

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)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(MCPAN)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/MCPAN/SCSrank.Rd_%03d_medium.png", width=480, height=480)
> ### Name: SCSrank
> ### Title: Compute a rectangular simultaneous confidence set from a sample
> ###   of a joint empirical distribution.
> ### Aliases: SCSrank
> ### Keywords: htest
> 
> ### ** Examples
> 
> 
> x <- cbind(rnorm(1000,1,2), rnorm(1000,0,2), rnorm(1000,0,0.5), rnorm(1000,2,1))
> dim(x)
[1] 1000    4
> 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)
$conf.int
         lower    upper
[1,] -6.709783 4.539878
[2,] -5.456775 3.006684
[3,] -3.628381 5.210104
attr(,"k")
[1] 900
attr(,"N")
[1] 1000

$conf.level
[1] 0.9

$alternative
[1] "two.sided"

> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>