Hypothesis testing in a generic nesting framework with general population distributions

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Editor: Universidad Carlos III de Madrid. Departamento de Estadística
Issued date: 2011-11
Serie-No.: UC3M Working papers. Statistics and Econometrics11-27
Keywords: Chi-bar-square statistic , Chi-square statistic , Divergence based test-statistics , Equality constraints , Exponential family of distributions , Inequality constraints
Rights: Atribución-NoComercial-SinDerivadas 3.0 España
Abstract:Nested parameter spaces, either in the null or alternative hypothesis, constitute aguarantee for improving the performance of the tests, however in the existing literatureon order restricted inference they have been usually skipped for being studied in detNested parameter spaces, either in the null or alternative hypothesis, constitute aguarantee for improving the performance of the tests, however in the existing literatureon order restricted inference they have been usually skipped for being studied in detail.Divergence based divergence measures provide a flexible tool for creating meaningfultest-statistics, which usually contain the likelihood ratio-test statistics as special case.The existing literature on hypothesis testing with inequality constraints using phidivergencemeasures, is centered in a very specific models with multinomial sampling.The contribution of this paper consists in extending and unifying widely the existingwork: new families of test-statistics are presented, valid for nested parameter spacescontaining either equality or inequality constraints and general distributions for eithersingle or multiple populations are considered.+-
Autor: Martín, Nirian; Balakrishnan, Narayanaswami
Fuente: http://e-archivo.uc3m.es
Introducción
Universidad Carlos III de Madrid
Repositorio institucional e-Archivo
http:--e-archivo.uc3m.es
Departamento de Estadística
DES - Working Papers.
Statistics and Econometrics.
WS
2011-11
Hypothesis testing in a generic nesting
framework with general population distributions
Martín, Nirian
http:--hdl.handle.net-10016-12618
Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid
Working Paper 11-35
Statistics and Econometrics Series 27
November 2011
Departamento de Estadística
Universidad Carlos III de Madrid
Calle Madrid, 126
28903 Getafe (Spain)
Fax (34) 91 624-98-49
HYPOTHESIS TESTING IN A GENERIC NESTING FRAMEWORK WITH
GENERAL POPULATION DISTRIBUTIONS
Nirian Martín1, Narayanaswami Balakrishnan2
Abstract
Nested parameter spaces, either in the null or alternative hypothesis, constitute a
guarantee for improving the performance of the tests, however in the existing literature
on order restricted inference they have been usually skipped for being studied in detail.
Divergence based divergence measures provide a flexible tool for creating meaningful
test-statistics, which usually contain the likelihood ratio-test statistics as special case.
The existing literature on hypothesis testing with inequality constraints using phidivergence measures, is centered in a very specific models with multinomial sampling.
The contribution of this paper consists in extending and unifying widely the existing
work: new families of test-statistics are presented, valid for nested parameter spaces
containing either equality or inequality constraints and general distributions for either
single or multiple populations are considered.
Keywords: Chi-bar-square statistic, Chi-square statistic, Divergence based teststatistics, Equality constraints, Exponential family of distributions, Inequality
constraints.
1
Nirian Martín, Department of Statistics, Universidad Carlos III de Madrid, Spain;
Narawashami Balakrishnan, Department of Mathematics, McMaste...