Bartlett's correction and the bootstrap in normal linear regression models

Rayner, Robert K.

doi:10.1016/0165-1765(90)90011-o

Cited by 7 publications

(4 citation statements)

References 12 publications

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“…This provides an effective correction of LR test that is faster than a bootstrap assessment of the distribution of p‐values. Although this method is not new (Rocke , Rayner ), it seems to have been overlooked in practice. For non‐spatial models, Pinheiro and Bates (, p. 88) used a simple design to illustrate the biases of LR tests in linear mixed models, and Fig.…”

Section: Methodsmentioning

confidence: 99%

Testing environmental and genetic effects in the presence of spatial autocorrelation

2014

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Spatial autocorrelation is a well‐recognized concern for observational data in general, and more specifically for spatial data in ecology. Generalized linear mixed models (GLMMs) with spatially autocorrelated random effects are a potential general framework for handling these spatial correlations. However, as the result of statistical and practical issues, such GLMMs have been fitted through the undocumented use of procedures based on penalized quasi‐likelihood approximations (PQL), and under restrictive models of spatial correlation. Alternatively, they are often neglected in favor of simpler but more questionable approaches. In this work we aim to provide practical and validated means of inference under spatial GLMMs, that overcome these limitations. For this purpose, a new software is developed to fit spatial GLMMs. We use it to assess the performance of likelihood ratio tests for fixed effects under spatial autocorrelation, based on Laplace or PQL approximations of the likelihood. Expectedly, the Laplace approximation performs generally slightly better, although a variant of PQL was better in the binary case. We show that a previous implementation of PQL methods in the R language, glmmPQL, is not appropriate for such applications. Finally, we illustrate the efficiency of a bootstrap procedure for correcting the small sample bias of the tests, which applies also to non‐spatial models.

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Section: Methodsmentioning

confidence: 99%

Testing environmental and genetic effects in the presence of spatial autocorrelation

2014

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“…Williams (1986), Rocke (1989), Rayner (1990aRayner ( , 1990b, Eakin, McMillen and Buono (1990), Affleck-Graves and McDonald (1990), Martin (1990), Atkinson and Wilson (1992), and Rilstone and Veall (1996). Although long recognized as a useful alternative to standard asymptotic methods, the bootstrap only has an asymptotic justification when the null distribution of the test statistic involves nuisance parameters, hence the finite sample properties of bootstrap tests remain to be established.…”

Section: Introductionmentioning

confidence: 99%

Simulation based finite and large sample tests in multivariate regressions

Dufour

Khalaf

2002

Journal of Econometrics

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CIRANOLe CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisationsmembres, d'une subvention d'infrastructure du ministère de la Recherche, de la Science et de la Technologie, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO is a private non-profit organization incorporated under the Résumé / AbstractDans le contexte des modèles de régression multivariés (MLR), il est bien connu que les tests asymptotiques usuels tendent à rejeter trop souvent les hypothèse considérées. Dans cet article, nous proposons une méthode générale qui permet de construire des tests exacts pour des hypothèses possiblement non linéaires sur les coefficients de tels modèles. Pour le cas des hypothèse uniformes linéaires, nous présentons des résultats sur la distribution exacte de plusieurs statistiques de test usuelles. Ces dernières incluent le critère du quotient de vraisemblance (Wilks), de même que les critères de la trace et de la racine maximale. L'hypothèse de normalité des erreurs n'est pas requise pour la plupart des résultats présentés. Ceux-ci ont deux types de conséquences pour l'inférence statistique. Premièrement, l'invariance par rapport aux paramètres de nuisance signifie que l'on peut appliquer la technique des tests de Monte Carlo afin de construire des tests exacts pour les hypothèses uniformes linéaires. Deuxième-ment, nous montrons comment exploiter cette propriété afin d'obtenir des bornes sans paramètres de nuisance sur la distribution des statistiques de quotient de vraisemblance pour des hypothèses générales. Même si les bornes ne sont pas faciles à calculer par des moyens analytiques, on peut les simuler aisément et ainsi effectuer des tests de Monte Carlo à bornes. Nous présentons une expérience de simulation qui montre que ces bornes sont suffisamment serrées pour fournir des résultats concluants avec une forte probabilité. Nos résultats démontrent la valeur de ces bornes comme instrument à utiliser conjointement avec des méthodes d'inférence simulée plus traditionnelles (telles que le bootstrap paramétrique) que l'on peut appliquer lorsque le test à borne n'est pas concluant.

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“…Canepa and Rocke both used a nonparametric bootstrap. Rayner (1990) examined the application of a parametric bootstrap to approximate the Bartlett correction factor in normal linear regression models and showed that this approach gave accuracy to the order of O ( n −3/2 ).…”

Section: Introductionmentioning

confidence: 99%

Improvement of the quasi‐likelihood ratio test in ARMA models: some results for bootstrap methods

Canepa

Godfrey

2006

Journal Time Series Analysis

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Quasi-likelihood ratio tests for autoregressive moving-average (ARMA) models are examined. The ARMA models are stationary and invertible with white-noise terms that are not restricted to be normally distributed. The white-noise terms are instead subject to the weaker assumption that they are independently and identically distributed with an unspecified distribution. Bootstrap methods are used to improve control of the finite sample significance levels. The bootstrap is used in two ways: first, to approximate a Bartlett-type correction; and second, to estimate the p-value of the observed test statistic. Some simulation evidence is provided. The bootstrap p-value test emerges as the best performer in terms of controlling significance levels. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

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Bartlett's correction and the bootstrap in normal linear regression models

Cited by 7 publications

References 12 publications

Testing environmental and genetic effects in the presence of spatial autocorrelation

Testing environmental and genetic effects in the presence of spatial autocorrelation

Simulation based finite and large sample tests in multivariate regressions

Improvement of the quasi‐likelihood ratio test in ARMA models: some results for bootstrap methods

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