R: One Sample Location Test based on Marginal Ranks in the...

rank.ictest {ICSNP} | R Documentation

## One Sample Location Test based on Marginal Ranks in the Independent Component Model

### Description

marginal rank test for the location problem in the one sample case when the margins are assumed independent.

### Usage

    rank.ictest(X, ...)

    ## Default S3 method:
    rank.ictest(X, mu = NULL, scores = "rank", method = "approximation",
                n.simu = 1000, na.action = na.fail, ...)

    ## S3 method for class 'ics'
    rank.ictest(X, index = NULL, na.action = na.fail, ...)

### Arguments

`X` | a numeric data frame or matrix or an ics object.
`mu` | a vector indicating the hypothesized value of the location. NULL represents the origin.
`scores` | options are 'rank' for the signed rank test, 'sign' for the sign test and 'normal' for the normal score test.
`method` | defines the method used for the computation of the p-value. The possibilites are "approximation" (default), "simulation" or "permutation". Details below.
`n.simu` | if '`method`=simulation' or '`method`=permutation' this specifies the number of replications used in the simulation or permutation procedure.
`index` | an integer vector that gives the columns to choose from invariant coordinates form the 'ics' object. The default uses all columns.
`na.action` | a function which indicates what should happen when the data contain 'NA's. Default is to fail.
`...` | further arguments to be passed to or from methods.

### Details

The test is normally used to test for location in the symmetric independent component model.

By default the limiting distribution is used to compute the p-values. However for moderate sample sizes (N=50) was observed in Nordhausen et al. (2009) that the normal score test can be sometimes slightly biased. Therefore the argument `method` can be used to get p-values based on simulations from a multivariate normal under the null or by permuting the signs of the centered observations.

### Value

A list with class 'htest' containing the following components:

`statistic` | the value of the Q-statistic.
`parameter` | the degrees of freedom for the Q-statistic.
`p.value` | the p-value for the test.
`null.value` | the specified hypothesized value of the location.
`alternative` | a character string with the value 'two.sided'.
`method` | a character string indicating what type of test was performed.
`data.name` | a character string giving the name of the data.

### Author(s)

Klaus Nordhausen, klaus.nordhausen@uta.fi

### References

Nordhausen, K., Oja, H. and Paindaveine, D. (2009), Signed-rank tests for location in the symmetric independent component model, Journal of Multivariate Analysis, 100, 821–834.

### Examples

    set.seed(555)
    X <- cbind(rt(30,8), rnorm(30,0.5), runif(30,-3,3))
    mix.matrix <- matrix(c(3,2,1,2,4,-0.5,1,-0.5,2), ncol=3)
    X.mixed <- X %*% t(mix.matrix)
    ica.X <- ics(X, covOrigin, cov4, S2args = list(location = "Origin"))
    rank.ictest(ica.X)
    rank.ictest(ica.X, scores = "normal", method = "simu")
    rank.ictest(ics.components(ica.X), scores = "normal", method = "perm")
    rm(.Random.seed)

[Package ICSNP version 1.1-0 Index]