Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimating the J function without edge correction   The interaction between points in a spatial point process can be measured by
its empty space function F, its nearest-neighbour distance distribution
function G, and by combinations such as the J-function $J = (1-G)/(1-F)$. The
estimation of these functions is hampered by edge effects: the uncorrected,
empirical distributions of distances observed in a bounded sampling window W
give severely biased estimates of F and G. However, in this paper we show that
the corresponding {\em uncorrected} estimator of the function $J=(1-G)/(1-F)$
is approximately unbiased for the Poisson case, and is useful as a summary
statistic. Specifically, consider the estimate $\hat{J}_W$ of J computed from
uncorrected estimates of F and G. The function $J_W(r)$, estimated by
$\hat{J}_W$, possesses similar properties to the J function, for example
$J_W(r)$ is identically 1 for Poisson processes. This enables direct
interpretation of uncorrected estimates of J, something not possible with
uncorrected estimates of either F, G or K. We propose a Monte Carlo test for
complete spatial randomness based on testing whether $J_W(r)(r)\equiv 1$.
Computer simulations suggest this test is at least as powerful as tests based
on edge corrected estimators of J.

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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys