Locally Asymptotic Normality of Gibbs Models on a Lattice

We consider the statistical estimation problem of potential functions of Gibbs models on the plane lattice. We assume that the area on which a random point pattern is observed is sufficiently large and take an asymptotic point of view. The main result is to show the locally asymptotic normality of t...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	Advances in Applied Probability. - Applied Probability Trust. - 16(1984), 3, Seite 585-602
1. Verfasser:	Mase, Shigeru (VerfasserIn)
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	1984
Zugriff auf das übergeordnete Werk:	Advances in Applied Probability
Schlagworte:	Plane lattice Asymptotic theory Potential function Maximum likelihood estimator Moment estimator Philosophy Mathematics Physical sciences Behavioral sciences Biological sciences


LEADER	01000caa a22002652 4500
001	JST000684058
003	DE-627
005	20240619091232.0
007	cr uuu---uuuuu
008	150322s1984 xx \|\|\|\|\|o 00\| \|\|eng c
024	7		\|a 10.2307/1427288 \|2 doi
035			\|a (DE-627)JST000684058
035			\|a (JST)1427288
040			\|a DE-627 \|b ger \|c DE-627 \|e rakwb
041			\|a eng
100	1		\|a Mase, Shigeru \|e verfasserin \|4 aut
245	1	0	\|a Locally Asymptotic Normality of Gibbs Models on a Lattice
264		1	\|c 1984
336			\|a Text \|b txt \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
520			\|a We consider the statistical estimation problem of potential functions of Gibbs models on the plane lattice. We assume that the area on which a random point pattern is observed is sufficiently large and take an asymptotic point of view. The main result is to show the locally asymptotic normality of the Gibbs model under certain conditions. From this result we can show the optimality of the maximum likelihood estimator employing known results about locally asymptotic normal families, though a practical computation of the maximum likelihood estimator presents difficulties. An estimation procedure based on the method of moments is also proposed.
540			\|a Copyright 1984 Applied Probability Trust
650		4	\|a Plane lattice
650		4	\|a Asymptotic theory
650		4	\|a Potential function
650		4	\|a Maximum likelihood estimator
650		4	\|a Moment estimator
650		4	\|a Philosophy \|x Logic \|x Logical topics \|x Formal logic \|x Mathematical logic \|x Mathematical set theory \|x Lattice theory \|x Mathematical lattices
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Inferential statistics \|x Statistical estimation \|x Estimation methods \|x Estimators
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Inferential statistics \|x Statistical estimation \|x Estimation methods \|x Estimators \|x Maximum likelihood estimators
650		4	\|a Physical sciences \|x Physics \|x Mathematical physics \|x Potential theory \|x Harmonic functions
650		4	\|a Mathematics \|x Applied mathematics \|x Analytics \|x Analytical estimating \|x Maximum likelihood estimation
650		4	\|a Behavioral sciences \|x Psychology \|x Cognitive psychology \|x Cognitive processes \|x Thought processes \|x Reasoning \|x Inference
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Inferential statistics \|x Statistical estimation \|x Estimation methods
650		4	\|a Mathematics \|x Pure mathematics \|x Linear algebra \|x Vector analysis \|x Mathematical vectors
650		4	\|a Biological sciences \|x Ecology \|x Ecological modeling
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Probabilities
655		4	\|a research-article
773	0	8	\|i Enthalten in \|t Advances in Applied Probability \|d Applied Probability Trust \|g 16(1984), 3, Seite 585-602 \|w (DE-627)269247009 \|w (DE-600)1474602-5 \|x 00018678 \|7 nnns
773	1	8	\|g volume:16 \|g year:1984 \|g number:3 \|g pages:585-602
856	4	0	\|u https://www.jstor.org/stable/1427288 \|3 Volltext
856	4	0	\|u https://doi.org/10.2307/1427288 \|3 Volltext
912			\|a GBV_USEFLAG_A
912			\|a SYSFLAG_A
912			\|a GBV_JST
912			\|a GBV_ILN_11
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_90
912			\|a GBV_ILN_100
912			\|a GBV_ILN_110
912			\|a GBV_ILN_285
912			\|a GBV_ILN_374
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2018
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2938
912			\|a GBV_ILN_2947
912			\|a GBV_ILN_2949
912			\|a GBV_ILN_2950
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4346
912			\|a GBV_ILN_4392
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 16 \|j 1984 \|e 3 \|h 585-602