# mv.1sample.test: Multivariate Location Tests In MNM: Multivariate Nonparametric Methods. An Approach Based on Spatial Signs and Ranks

## Description

Tests for multivariate location using different score functions.

## Usage

 ```1 2 3``` ```mv.1sample.test(X, mu = 0, score = "identity", stand = "outer", method = "approximation", n.simu = 1000, na.action = na.fail) ```

## Arguments

 `X` a numeric data frame or matrix. `mu` the null hypothesis value. Default is the zero vector. `score` the score to be used. Possible choices are `identity`, `sign` and `rank`. `stand` the standardization method used. Possible choices are `outer` and `inner`. `method` method for the computation of the p-value for the spatial sign and spatial signed-rank tests. Possible choices are `approximation` and `signchange`. `n.simu` number of simulated sign changes if `method=signchange`. `na.action` a function which indicates what should happen when the data contain 'NA's. Default is to fail.

## Details

The tests provided here are the Hotelling's T^2 test, the spatial sign test and the signed-rank test and their affine invariant versions in the one sample location case.

Note that for the identity score the provided test is not the traditional Hotelling's T^2 test because here the covariance matrix is computed wrt to the null value and not wrt to the sample mean. Use the function `HotellingsT2` for the traditional version of Hotelling's T^2 test. Details about the tests can be found in the chapters 5-8 of the MNM book.

## Value

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

 `statistic ` the value of the test statistic. `parameter` the degrees of freedom for the test statistic or the number of replications in the simulation. `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 set.

Klaus Nordhausen

## References

Oja, H. (2010), Multivariate Nonparametric Methods with R, Springer.

Nordhausen, K. and Oja, H. (2011), Multivariate L1 Methods: The Package MNM, Journal of Statistical Software, 43, 1-28.

`HotellingsT2`, `sr.loc.test`
 ```1 2 3 4 5 6 7 8``` ```library(mvtnorm) X <- rmvt(100, diag(c(1, 2, 0.5)), 3) mv.1sample.test(X,mu=c(0,0,0.5)) mv.1sample.test(X,score="s", stand="i") mv.1sample.test(X,score="s", stand="i", method="s") mv.1sample.test(X,score="r", stand="o") mv.1sample.test(X,score="r", stand="i") ```