Let \(X\) denote a continuous random variable, then the following model
with a single shift (change-point) can be proposed:
$$
x_i = \left\{
\begin{array}{lcl}
\theta + \epsilon_i, & \qquad & i = 1, \ldots, m \\
\theta + \Delta + \epsilon_i & \qquad & i = m + 1, \ldots, n \\
\end{array} \right.$$
with \(\theta(\epsilon) = 0\). The null hypothesis, H:\(\Delta = 0\)
is tested against the alternative A:\(\Delta \ne 0\).
First, the data are transformed into increasing ranks
and for each time-step the adjusted rank sum is computed:
$$U_k = 2 \sum_{i=1}^k r_i - k \left(n + 1\right) \qquad k = 1, \ldots, n$$
The probable change point is located at the absolute maximum
of the statistic:
$$m = k(\max |U_k|)$$.
For method = "wilcox.test" the Wilcoxon-Mann-Whitney two-sample
test is performed, using \(m\) to split the series. Otherwise,
the robust rank-order distributional test (rrod.test is
performed.