Dear All,

I would like to estimate 
let say  95th percentile of  the distribution of
\tau=max|\hat
 L(r)-r| for r<=r0. 




using Monte Carlo simulation (the number of 
simulation is
20000) for a Binomial point pattern with n point in a unit square, for  different n, let say n=10,20,25,30,40,50,100,200,300 and known value of r0.


    


To proceed we estimate the Ripley K-function  using R package “spatstat” .

I need please some technical comments, describing 
me the  “Truth” of  the 
following statements about using spatstat
function “Kest”. “Note that 
empirical K function is a

step function and hence the max occurs 
only at a jump point. The

default output of the spatstat package 
reports the estimated K at

regular intervals and hence the max at 
these regular points is close to

but not exactly the real max we have in
 mind. The importance of using

the exact real max is to make sure that
 everyone will get the same

value. If we use a sequence of regular 
lattice points, the value

depends on the lattice size. Note also 
if you use the same regular

points to find the max for different n,
 then the larger the value n, the

poor the accuracy of the max 
approximated by the max at the regular points.”



Many thanks in advance
Hamid



      
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