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

Great, thanks so much for taking the time to answer this Adrian! And for
the book link!

On Wed, Jul 27, 2016 at 3:25 AM Adrian Baddeley <
adrian.baddeley at curtin.edu.au> wrote:

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