On testing of general random closed set model hypothesis

Mrkvička, Tomáš. "On testing of general random closed set model hypothesis." Kybernetika 45.2 (2009): 293-308. <http://eudml.org/doc/37727>.

@article{Mrkvička2009,
abstract = {A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set $\Xi \subseteq \{\{\mathbb \{R\}\}^d\}$ with values in the extended convex ring is introduced. The method is based on the summary statistics – normalized intrinsic volumes densities of the $\varepsilon $-parallel sets to $\Xi $. The estimated summary statistics are compared with theirs envelopes produced from simulations of the model given by the tested hypothesis. The p-level of the test is then computed via approximation of the summary statistics by multinormal distribution which mean and the correlation matrix is computed via given simulations. A new estimator of the intrinsic volumes densities from [6] is used, which is especially suitable for estimation of the intrinsic volumes densities of $\varepsilon $-parallel sets. The power of this test is estimated for planar Boolean model hypothesis and two different alternatives and the resulted powers are compared to the powers of known Boolean model tests. The method is applied on the real data set of a heather incidence.},
author = {Mrkvička, Tomáš},
journal = {Kybernetika},
keywords = {Boolean model; Boolean model hypothesis; contact distribution function; Euler–Poincaré characteristic; Intrinsic volumes; Laslettś transform; Boolean model; Boolean model hypothesis; contact distribution function; Euler-Poincaré characteristic; intrinsic volumes; Laslett's transform; heather incidence data},
language = {eng},
number = {2},
pages = {293-308},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On testing of general random closed set model hypothesis},
url = {http://eudml.org/doc/37727},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Mrkvička, Tomáš
TI - On testing of general random closed set model hypothesis
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 2
SP - 293
EP - 308
AB - A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set $\Xi \subseteq {{\mathbb {R}}^d}$ with values in the extended convex ring is introduced. The method is based on the summary statistics – normalized intrinsic volumes densities of the $\varepsilon $-parallel sets to $\Xi $. The estimated summary statistics are compared with theirs envelopes produced from simulations of the model given by the tested hypothesis. The p-level of the test is then computed via approximation of the summary statistics by multinormal distribution which mean and the correlation matrix is computed via given simulations. A new estimator of the intrinsic volumes densities from [6] is used, which is especially suitable for estimation of the intrinsic volumes densities of $\varepsilon $-parallel sets. The power of this test is estimated for planar Boolean model hypothesis and two different alternatives and the resulted powers are compared to the powers of known Boolean model tests. The method is applied on the real data set of a heather incidence.
LA - eng
KW - Boolean model; Boolean model hypothesis; contact distribution function; Euler–Poincaré characteristic; Intrinsic volumes; Laslettś transform; Boolean model; Boolean model hypothesis; contact distribution function; Euler-Poincaré characteristic; intrinsic volumes; Laslett's transform; heather incidence data
UR - http://eudml.org/doc/37727
ER -