Plane Answers to Complex Questions : The Theory of Linear Models / by Ronald Christensen
(Springer Texts in Statistics)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1987 |
| 本文言語 | 英語 |
| 大きさ | XIV, 380 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | *Christensen, Ronald author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Applied mathematics LCSH:Engineering mathematics FREE:Mathematics FREE:Applications of Mathematics |
| 分 類 | DC23:519 |
| 巻冊次 | ISBN:9781475719512 
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| ISBN | 9781475719512 |
| URL | http://dx.doi.org/10.1007/978-1-4757-1951-2 |
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