# Test

Main Page > Test
Parallel

## Überschrift 2

### Überschrift 2.2

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[1] 2 6 3
[1] 1 2 3
x y
[1,] 2 1
[2,] 6 2
[3,] 3 3
[,1] [,2] [,3]
x    2    6    3
y    1    2    3

Submit form "test" ?

<textarea name="mydata"> 1 2 3 </textarea> <input type="submit" value=" Submit ">

[1] 9

## Package info

 Package abind Version 1.1-0 Date 2004-03-12 Title Combine multi-dimensional arrays Author Tony Plate and Richard Heiberger Maintainer Tony Plate Description Combine multi-dimensional arrays. This is a generalization of cbind and rbind. Takes a sequence of vectors, matrices, or arrays and produces a single array of the same or higher dimension. Depends R (>= 1.5.0) License LGPL Version 2 or later.

## Functions

Function(s) Description Keyword(s)
abind Combine multi-dimensional arrays. This is a generalization of cbind and rbind. Takes a sequence of vectors, matrices, or arrays and produces a single array of the same or higher dimension.
adrop Drop degenerate dimensions of an array object. Offers more control than the drop() function. control

## Package functions

Package Function Description
adegenet monmonier The Monmonier's algorithm detects boundaries among vertices of a valuated graph. This is achieved by finding the path exhibiting the largest distances between connected vertices.cr The highest distance between two connected vertices (i.e. neighbours) is found, giving the starting point of the path. Then, the algorithm seeks the highest distance between immediate neighbours, and so on until a threshold value is attained. This threshold can be chosen from the plot of sorted distances between connected vertices: a boundary will likely result in an abrupt decrease of these values.cr When several paths are looked for, the previous paths are taken into account, and cannot be either crossed or redrawn. Monmonier's algorithm can be used to assess the boundaries between patches of homogeneous observations.cr Although Monmonier algorithm was initially designed for Voronoi tesselation, this implementation generalizes this algorithm to different connection networks. The optimize.monmonier function produces a monmonier object by trying several starting points, and returning the best boundary (i.e. largest sum of local distances). This is designed to avoid the algorithm to be trapped by a single strong local difference inside an homogeneous patch.
adehabitat labcon This function attributes unique labels to pixels belonging to connected features on a map of class asc.

## Linear Hypothesis

In this section, we present a very general procedure which allows a linear hypothesis to be tested, i.e., a linear restriction, either on a vector mean $\mu$ or on the coefficient $\beta$ of a linear model. The presented technique covers many of the practical testing problems on means or regression coefficients.

Linear hypotheses are of the form $\data{A}\mu =a$ with known matrices $\data{A}(q\times p)$ and $a (q\times 1)$ with $q \le p$.

EXAMPLE 7.7   Let $\mu=(\mu_{1},\mu_{2})^{\top}$. The hypothesis that $\mu_{1}=\mu_{2}$ can be equivalently written as:

The general idea is to test a normal population $H_0:\; {\cal{A}}\mu=a$ (restricted model) against the full model $H_1$ where no restrictions are put on $\mu$. Due to the properties of the multinormal, we can easily adapt the Test Problems 1 and 2 to this new situation. Indeed we know, from Theorem 5.2, that $y_i={\cal{A}}x_i \sim N_q(\mu_y,\Sigma_y)$, where $\mu_y={\cal{A}}\mu$ and $\Sigma_y={\cal{A}}\Sigma{\cal{A}}^{\top}$.

Testing the null $H_0:\; {\cal{A}}\mu=a$, is the same as testing $H_0:\; \mu_y=a$. The appropriate statistics are $\bar y$ and ${\cal{S}}_y$ which can be derived from the original statistics $\bar x$ and ${\cal{S}}$ available from ${\cal{X}}$: