Christensen Plane Answers to Complex Questions

The Theory of Linear Models
1987
ISBN: 978-1-4757-1951-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 380 Seiten, eBook

Reihe: Springer Texts in Statistics

This book was written to rigorously illustrate the practical application of the projective approach to linear models. To some, this may seem contradictory. I contend that it is possible to be both rigorous and illustrative and that it is possible to use the projective approach in practical applications. Therefore, unlike many other books on linear models, the use of projections and sub spaces does not stop after the general theory. They are used wherever I could figure out how to do it. Solving normal equations and using calculus (outside of maximum likelihood theory) are anathema to me. This is because I do not believe that they contribute to the understanding of linear models. I have similar feelings about the use of side conditions. Such topics are mentioned when appropriate and thenceforward avoided like the plague. On the other side of the coin, I just as strenuously reject teaching linear models with a coordinate free approach. Although Joe Eaton assures me that the issues in complicated problems frequently become clearer when considered free of coordinate systems, my experience is that too many people never make the jump from coordinate free theory back to practical applications. I think that coordinate free theory is better tackled after mastering linear models from some other approach. In particular, I think it would be very easy to pick up the coordinate free approach after learning the material in this book. See Eaton (1983) for an excellent exposition of the coordinate free approach.

Zielgruppe

Research

Autoren/Hrsg.

Christensen, Ronald

Inhaltsverzeichnis

I. Introduction.- II. Estimation.- III. Testing Hypotheses.- IV. One-Way ANOVA.- V. Multiple Comparison Techniques.- VI. Regression Analysis.- VII. Multifactor Analysis of Variance.- VIII. Experimental Design Models.- IX. Analysis of Covariance.- X. Estimation and Testing in a General Gauss-Markov Model.- XI. Split Plot Models.- XII. Mixed Models and Variance Components.- XIII. The Analysis of Residuals and Influential Observations in Regression.- XIV. Additional Topics in Regression: Variable Selection and Collinearity.- XV. Maximum Likelihood Theory for Log-Linear Models.- Appendix A: Vector Spaces.- Appendix B: Matrices.- Appendix C: Some Univariate Distributions.- Appendix D: Multivariate Distributions.- Appendix E: Tests and Confidence Intervals for Some One Parameter Problems.- Appendix F: Approximate Methods for Unbalanced ANOVA’s.- Appendix G: Randomization Theory Models.- References.- Author Index.