Author | Getson, Albert J. author |
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Title | {2}-Inverses and Their Statistical Application [electronic resource] / by Albert J. Getson, Francis C. Hsuan |
Imprint | New York, NY : Springer New York, 1988 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3930-7 |
Descript | VIII, 110 p. online resource |
I Introduction -- II Time for {2}-Inverses -- 2.0 Introduction -- 2.1 The Three Phase Inversion Procedure -- 2.2 Constrained Inverses -- 2.3 {2}- and {1,2}-Inverses: The Null Augmented Mappings -- 2.4 {1,5}-Inverses: The Nonnull Augmented Mappings -- 2.5 Construction of Moore-Penrose Type Generalized Inverses -- 2.6 A Geometric Representation of {2}-Inverses -- 2.7 {1,5}-Inverses and Projections -- 2.8 {1,5}-Inverses and Solutions to Linear Equations -- 2.9 Decomposition of {2}-Inverses -- 2.10 Spectral Decomposition in Terms of {2}Inverses -- 2.11 Computation of {2}-Inverses -- III {2}-Inverses, Quadratic Forms and Second Degree Polynomials -- 3.0 Introduction -- 3.1 x2 Distribution and Independence of Quadratic Forms and Second Degree Polynomials -- 3.2 Generalized Inverses and Quadratic Forms -- 3.3 {2}-Inverses and x2 Distributed Quadratic Forms -- 3.4 On The Uniqueness of the {2}-Inverse Representation of x2 Distributed Quadratic Forms -- 3.5 A Minimal Sufficient Set of Coefficient Matrices for All X2 Distributed Quadratic Forms -- 3.6 Independence of X2 Distributed Quadratic Forms -- 3.7 A Canonical Representation of Second Degree Polynomials -- 3.8 X2 Distributed Second Degree Polynomials -- 3.9 {2}-Inverses and the Distribution and Independence of Second Degree Polynomials -- IV {2}-Inverses and Least Squares Solutions -- 4.0 Introduction -- 4.1 The Least Squares Problem -- 4.1 Strategies For Obtaining Least Squares Solutions -- 4.3 Symmetric {1,2}-Inverses and Sets of Nonestimable Constraints -- 4.4 Bott-Duffin Inverses and Constrained LSSโs -- 4.5 {1,5}-Inverses and LSSโs -- 4.6 Relationships Among LSSโs -- 4.7 Minimum Norm LSSโs -- 4.8 A General Theorem on Constrained LSSโs -- 4.9 Residual Sum of Squares and Their Difference -- 4.10 Computing Constrained LSSโs and Residual Sum of Squares -- V {2}-Inverses in Linear Models -- 5.0 Introduction -- 5.1 The Models -- 5.2 The Distribution and Relationships Among the LSSโs For the Prameters in Various Models -- 5.3 Hypothesis Testing in Linear Models -- 5.4 Equivalent Numerator Sum of Squares for a Test of Hypothesis -- 5.5 Hypotheses Invariant to Cell Sizes -- 5.6 The R Approach and SAS Type I and Type II Sums of Squares -- 5.7 The R* Approach and the SAS Type III Sum of Squares -- References