Within spatial statistics, there exists an L-hat function, which to my understanding is a square-root transformed estimate of Ripley's K-function. However, I am trying to understand if there is another form of the L-function, as to my understanding the tilde represents a competing estimate. If there is such a statistic, how is it defined?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
I'm not aware of such a "competing estimate". The K-function (without any hat or tilde) is a theoretically defined function which for a stationary process has something to do with the mean number of neighbours in a ball of radius $r$ around a "typical point of the process" (specifically $\lambda K(r)$ gives you this mean number, where $\lambda$ is the intensity of the process).
Then for a process in the plane ($d=2$) Besag defined the L-function (no hat or tilde) as $L(r) = \sqrt{K(r)/\pi}$.
There are many different ways to estimate the K-function (typically differing by edge correction method). Given such an estimate $\hat K(r)$ the L-function is then estimated as $\hat L(r) = \sqrt{\hat K(r)/\pi}$. I have never seen other estimates for the L-function, but maybe you have seen two different estimates based on two different edge corrections for the K-function, and somebody named one of them $\tilde L$?
Alternatively if you want the analogue of the L-function in higher dimension you cannot simply use the squareroot, so maybe somebody defined an L-function in e.g. $d=3$ and called it $\tilde L$?
