Higher-Order Asymptotic Normality of Approximations to the Modified Signed Likelihood Ratio Statistic for Regular Models

Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n⁻¹, where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as ($\hat{\theta}$, a), where $\hat{\theta}$ is the max...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	The Annals of Statistics. - Institute of Mathematical Statistics. - 35(2007), 5, Seite 2054-2074
1. Verfasser:	He, Heping (VerfasserIn)
Weitere Verfasser:	Severini, Thomas A.
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2007
Zugriff auf das übergeordnete Werk:	The Annals of Statistics
Schlagworte:	Edgeworth expansion theory Modified signed likelihood ratio statistic Higher-order normality Sufficient statistic Cramér-Edgeworth polynomial Mathematics Behavioral sciences


LEADER	01000caa a22002652 4500
001	JST008981418
003	DE-627
005	20240619180803.0
007	cr uuu---uuuuu
008	150323s2007 xx \|\|\|\|\|o 00\| \|\|eng c
035			\|a (DE-627)JST008981418
035			\|a (JST)25464573
040			\|a DE-627 \|b ger \|c DE-627 \|e rakwb
041			\|a eng
084			\|a 62F05 \|2 MSC
084			\|a 62F03 \|2 MSC
100	1		\|a He, Heping \|e verfasserin \|4 aut
245	1	0	\|a Higher-Order Asymptotic Normality of Approximations to the Modified Signed Likelihood Ratio Statistic for Regular Models
264		1	\|c 2007
336			\|a Text \|b txt \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
520			\|a Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n⁻¹, where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as ($\hat{\theta}$, a), where $\hat{\theta}$ is the maximum likelihood estimator of the parameter θ of the model and a is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statistics themselves does not require this condition. The goal of this paper is to provide conditions under which these statistics are asymptotically normally distributed to order n⁻¹ without making any assumption about the sufficient statistic of the model.
540			\|a Copyright 2007 Institute of Mathematical Statistics
650		4	\|a Edgeworth expansion theory
650		4	\|a Modified signed likelihood ratio statistic
650		4	\|a Higher-order normality
650		4	\|a Sufficient statistic
650		4	\|a Cramér-Edgeworth polynomial
650		4	\|a Mathematics \|x Mathematical procedures \|x Approximation
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics
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 Mathematics \|x Mathematical values \|x Ratios
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables
650		4	\|a Mathematics \|x Pure mathematics \|x Algebra \|x Polynomials
650		4	\|a Mathematics \|x Mathematical objects \|x Mathematical series \|x Power series \|x Taylor series
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Statistical models \|x Parametric models
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 Mathematical values \|x Mathematical variables \|x Mathematical independent variables
650		4	\|a Mathematics \|x Mathematical procedures \|x Approximation
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics
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 Mathematics \|x Mathematical values \|x Ratios
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables
650		4	\|a Mathematics \|x Pure mathematics \|x Algebra \|x Polynomials
650		4	\|a Mathematics \|x Mathematical objects \|x Mathematical series \|x Power series \|x Taylor series
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Statistical models \|x Parametric models
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 Mathematical values \|x Mathematical variables \|x Mathematical independent variables
655		4	\|a research-article
700	1		\|a Severini, Thomas A. \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t The Annals of Statistics \|d Institute of Mathematical Statistics \|g 35(2007), 5, Seite 2054-2074 \|w (DE-627)270129162 \|w (DE-600)1476670-X \|x 00905364 \|7 nnns
773	1	8	\|g volume:35 \|g year:2007 \|g number:5 \|g pages:2054-2074
856	4	0	\|u https://www.jstor.org/stable/25464573 \|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_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
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_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_374
912			\|a GBV_ILN_602
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_2111
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2932
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_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
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_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4346
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 35 \|j 2007 \|e 5 \|h 2054-2074