[R-sig-Geo] Isotropic edge correction unbiasedness

[Adrian Baddeley]

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




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