Isotropic edge correction unbiasedness
Nick Eubank writes:
Using `kest` to estimate a ripley's K for a country.
This is a question about the 'spatstat' package. The function name is 'Kest'.
The authors of the package suggest isotropic is best when computationally tractable for irregular shapes, but I noticed in Ripley (1988) that this correction is only "unbiased provided E is convex", where E is the boundaries of study.
This is covered at length in Chapter 7 of the 'spatstat book' <https://www.crcpress.com/Spatial-Point-Patterns-Methodology-and-Applications-with-R/Baddeley-Rubak-Turner/p/book/9781482210200 The isotropic corrected estimate is unbiased for all r < R, where R is the radius of the smallest circle that encloses the entire window (assuming the window is connected).
With that said, the picture in Ripley (1988) illustrating this correction is NOT convex (it's a kidney shape).
So the statement above applies to this window.
I know this isn't quite an "r-implementation" question, but: anyone know if isotropic correction is unbiased for an odd shape like a country-outline (in this case Sweden)? Or should i use the `border` correction?
Use the isotropic correction. Adrian Baddeley