About: On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	A method of estimation of intrinsic volume densities for stationary random closed sets based on estimating volumes of tiny collars has been introduced in T. Mrkvi\v cka and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch.\ Proc.\ Appl.\ 118/2 (2008), 213--231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation radii in the discrete approximation, which differs from the standard techniques used for measuring parallel sets in image analysis. A method of reducing the bias is proposed and tested on simulated data. A method of estimation of intrinsic volume densities for stationary random closed sets based on estimating volumes of tiny collars has been introduced in T. Mrkvi\v cka and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch.\ Proc.\ Appl.\ 118/2 (2008), 213--231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation radii in the discrete approximation, which differs from the standard techniques used for measuring parallel sets in image analysis. A method of reducing the bias is proposed and tested on simulated data. (en)
Title	On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane (en)
skos:prefLabel	On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane (en)
skos:notation	RIV/00216208:11320/09:10051947!RIV11-GA0-11320___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/06/0302), P(KJB101420801), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	6
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Rataj, Jan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	331383
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/09:10051947
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	random closed set, convex ring, curvature measure, intrinsic volume (en)
http://linked.open.../riv/klicoveSlovo	convex ring curvature measure intrinsic volume random closed set
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[77221EF3AFFE]
http://linked.open...i/riv/nazevZdroje	Kybernetika
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Construction of Statistical Tests in Spatial Statistics Applied probability - stochastic geometry and metric tools
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	45
http://linked.open...iv/tvurceVysledku	Mrkvička, Tomáš Rataj, Jan
http://linked.open...ain/vavai/riv/wos	000275281200004
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	0023-5954
number of pages	15 (xsd:int)
http://localhost/t...ganizacniJednotka	11320

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