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Weight Matrices (weight + matrix)

Distribution by Scientific Domains
Mathematics and Statistics50%

Selected Abstracts

Augmentation block preconditioners for saddle point-type matrices with singular (1, 1) blocks

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 6 2008
Zhi-Hao Cao
Abstract We consider the use of block preconditioners for the application of the preconditioned Krylov subspace iterative methods to the solution of large saddle point-type systems with singular (1, 1) blocks. Two block triangular preconditioners are introduced and the block diagonal preconditioner in Greif and Schötzau (Electron. Trans. Numer. Anal. 2006; 22:114,121) is extended to nonsymmetric saddle point systems. All these preconditioners are based on augmentation, using nonsingular weight matrices. If the nullity of the (1, 1) block takes its highest possible value, the preconditioned matrix with either block triangular preconditioner has precisely three distinct eigenvalues, and the preconditioned matrix with the block diagonal preconditioner has precisely two distinct eigenvalues, giving rise to immediate convergence of preconditioned GMRES. Finally, numerical experiments that validate the analysis are reported. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Specification issues in models of population and employment growth*

PAPERS IN REGIONAL SCIENCE, Issue 1 2005
Marlon G. Boarnet
Spatial econometrics; population and employment growth Abstract., This article examines two specification issues common to spatial econometric population-employment growth models: the specification of the weight matrix and the dynamic stability implied by estimated lag parameters. Using data on Orange County census tracts from 1980 to 1990, we estimate a simultaneous system of regressions for tract population and employment growth. Six different weight matrices are tested, ranging from simple contiguity matrices to more complex matrices based on commute flows between census tracts. We also examine whether the inclusion of detailed information on land use improves performance of the lagged adjustment model. The results provide insights for future applications of econometric population-employment growth models. We found that the estimated lag parameters were consistent with dynamic stability for the models that included detailed land use data. Results varied for different weight matrices, but variation was mostly confined to interaction between population and employment growth. [source]

Modified weights based generalized quasilikelihood inferences in incomplete longitudinal binary models

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2010
Brajendra C. Sutradhar
Abstract In an incomplete longitudinal set up, a small number of repeated responses subject to an appropriate missing mechanism along with a set of covariates are collected from a large number of independent individuals over a small period of time. In this set up, the regression effects of the covariates are routinely estimated by solving certain inverse weights based generalized estimating equations. These inverse weights are introduced to make the estimating equation unbiased so that a consistent estimate of the regression parameter vector may be obtained. In the existing studies, these weights are in general formulated conditional on the past responses. Since the past responses follow a correlation structure, the present study reveals that if the longitudinal data subject to missing mechanism are generated by accommodating the longitudinal correlation structure, the conditional weights based on past correlated responses may yield biased and hence inconsistent regression estimates. The bias appears to get larger as the correlation increases. As a remedy, in this paper the authors proposed a modification to the formulation of the existing weights so that weights are not affected directly or indirectly by the correlations. They have then exploited these modified weights to form a weighted generalized quasi-likelihood estimating equation that yields unbiased and hence consistent estimates for the regression effects irrespective of the magnitude of correlation. The efficiencies of the regression estimates follow due to the use of the true correlation structure as a separate longitudinal weights matrix in the estimating equation. The Canadian Journal of Statistics © 2010 Statistical Society of Canada Dans un cadre de données longitudinales incomplètes, nous observons un petit nombre de réponses répétées sujettes à un mécanisme de valeurs manquantes approprié avec un ensemble de covariables provenant d'un grand nombre d'individus indépendants observés sur une petite période de temps. Dans ce cadre, les composantes de régression des covariables sont habituellement estimées en résolvant certains poids inverses obtenus à partir d'équations d'estimation généralisées. Ces poids inverses sont utilisés afin de rendre les équations d'estimation sans biais et ainsi permettre d'obtenir des estimateurs cohérents pour le vecteur des paramètres de régressions. Dans les études déjà existantes, ces poids sont généralement formulés conditionnement aux réponses passées. Puisque les réponses passées possèdent une structure de corrélation, cet article révèle que si les données longitudinales, soumises à un mécanisme de valeurs manquantes, sont générées en adaptant la structure de corrélation longitudinale, alors les poids conditionnels basés sur les réponses corrélées passées peuvent mener à des estimations biaisées, et conséquemment non cohérentes, des composantes de régression. Ce biais semble augmenter lorsque la corrélation augmente. Pour remédier à cette situation, les auteurs proposent dans cet article, une modification aux poids déjà existants afin que ceux-ci ne soient plus affectés directement ou indirectement par les corrélations. Par la suite, ils ont exploité ces poids modifiés pour obtenir une équation d'estimation généralisée pondérée basée sur la quasi-vraisemblance qui conduit à des estimateurs sans biais, et ainsi cohérents, pour les composantes de régression sans égard à l'ampleur de la corrélation. L'efficacité de ces estimateurs est attribuable à l'utilisation de la vraie structure de corrélation comme matrice de poids longitudinale à part dans l'équation d'estimation. La revue canadienne de statistique © 2010 Société statistique du Canada [source]