I am just beginng an investigation involving characterizing the dependence between two 1D stochastic point processes $x$, $y$. The natural approach seems to involve Ripley's K-function:
$$ K(t) = \frac{T}{n_xn_y} \sum_{i=1}^{n_x} \sum_{j=1}^{n_y} w(x_i,y_j) I[d(x_i,y_j)<t] $$
where $n_x$ is the number of observations in $x$ and $n_y$ is the number of observations in $y$ across the interval $T$. Deviation from $K(t)=t $ is an indication of correlation between the two point processes.
However, it's not clear to me how to estimate the edge correction $w(x_i,y_j)$ the 1D case. Some papers refer to Hani Doss' 1989 papers, but in the JSTOR paper he explicity states that ' this edge correction will not concern us.' FWIW-I am currently using a correction weight of 2, but intuitively that seems excessive in my case.
