The linear model and hypothesis a general unifying theory / [electronic resource] :

• 作者： Seber, George A.F.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Springer series in statistics
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Springer series in statistics
• 主題： Linear models (Statistics) , Statistical hypothesis testing , Mathematical statistics , Statistics , Statistical Theory and Methods. , Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law.
• ISBN： 9783319219301 (electronic bk.) 、 9783319219295 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 1.Preliminaries -- 2. The Linear Hypothesis -- 3.Estimation -- 4.Hypothesis Testing -- 5.Inference Properties -- 6.Testing Several Hypotheses -- 7.Enlarging the Model -- 8.Nonlinear Regression Models -- 9.Multivariate Models -- 10.Large Sample Theory: Constraint-Equation Hypotheses -- 11.Large Sample Theory: Freedom-Equation Hypotheses -- 12.Multinomial Distribution -- Appendix -- Index.
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• 摘要註: This book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The approach used is a geometrical one based on the concept of projections and their associated idempotent matrices, thus largely avoiding the need to involve matrix ranks. It is shown that all the hypotheses encountered are either linear or asymptotically linear, and that all the underlying models used are either exactly or asymptotically linear normal models. This equivalence can be used, for example, to extend the concept of orthogonality in the analysis of variance to other models, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.
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