Atnaujinkite slapukų nuostatas

Primer on Linear Models [Minkštas viršelis]

3.50/5 (4 ratings by Goodreads)
(North Carolina State University, Raleigh, USA)
  • Formatas: Paperback / softback, 304 pages, aukštis x plotis: 234x156 mm, weight: 560 g, 2 Tables, black and white; 6 Illustrations, black and white
  • Serija: Chapman & Hall/CRC Texts in Statistical Science
  • Išleidimo metai: 31-Mar-2008
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1420062018
  • ISBN-13: 9781420062014
Kitos knygos pagal šią temą:
Primer on Linear ModelsDidesnis paveikslėlis
  • Formatas: Paperback / softback, 304 pages, aukštis x plotis: 234x156 mm, weight: 560 g, 2 Tables, black and white; 6 Illustrations, black and white
  • Serija: Chapman & Hall/CRC Texts in Statistical Science
  • Išleidimo metai: 31-Mar-2008
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1420062018
  • ISBN-13: 9781420062014
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781420062014.html
Raktažodžiai:
A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods.

With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the GaussMarkov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers.

This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models.

Recenzijos

"I found the book very helpful. ā¦ the result is very nice, very readable. In particular, I like the idea of avoiding leaps in the development and proofs, or referring to other sources for the details of the proofs. This is a useful well-written instructive book." ~International Statistical Review

"This work provides a brief, and also complete, foundation for the theory of basic linear models . . . can be used for graduate courses on linear models."

~Nicoleta Breaz, Zentralblatt Math

". . . well written . . . would serve well as the textbook for an introductory course in linear models, or as references for researchers who would like to review the theory of linear models." ~Justine Shults, Journal of Biopharmaceutical Statistics "I found the book very helpful. ā¦ the result is very nice, very readable. In particular, I like the idea of avoiding leaps in the development and proofs, or referring to other sources for the details of the proofs. This is a useful well-written instructive book." ~International Statistical Review

"This work provides a brief, and also complete, foundation for the theory of basic linear models . . . can be used for graduate courses on linear models."

~Nicoleta Breaz, Zentralblatt Math

". . . well written . . . would serve well as the textbook for an introductory course in linear models, or as references for researchers who would like to review the theory of linear models." ~Justine Shults, Journal of Biopharmaceutical Statistics

Preface xiii
Examples of the General Linear Model
1(12)
Introduction
1(1)
One-Sample Problem
1(1)
Simple Linear Regression
2(1)
Multiple Regression
2(1)
One-Way Anova
3(1)
First Discussion
4(1)
Two-Way Nested Model
5(1)
Two-Way Crossed Model
6(2)
Analysis of Covariance
8(1)
Autoregression
8(1)
Discussion
9(1)
Summary
10(1)
Notes
10(1)
Exercises
11(2)
The Linear Least Squares Problem
13(24)
The Normal Equations
13(2)
The Geometry of Least Squares
15(8)
Reparameterization
23(4)
Gram-Schmidt Orthonormalization
27(3)
Summary of Important Results
30(1)
Notes
30(1)
Exercises
31(6)
Estimability and Least Squares Estimators
37(34)
Assumptions for the Linear Mean Model
37(1)
Confounding, Identifiability, and Estimability
37(1)
Estimability and Least Squares Estimators
38(3)
First Example: One-Way Anova
41(4)
Second Example: Two-Way Crossed without Interaction
45(3)
Two-Way Crossed with Interaction
48(2)
Reparameterization Revisited
50(6)
Imposing Conditions for a Unique Solution to the Normal Equations
56(4)
Constrained Parameter Space
60(4)
Summary
64(1)
Exercises
64(7)
Gauss-Markov Model
71(28)
Model Assumptions
71(2)
The Gauss-Markov Theorem
73(2)
Variance Estimation
75(1)
Implications of Model Selection
76(6)
Underfitting or Misspecification
77(2)
Overfitting and Multicollinearity
79(3)
The Aitken Model and Generalized Least Squares
82(5)
Estimability
82(1)
Linear Estimator
83(1)
Generalized Least Squares Estimators
83(1)
Estimation of σ2
83(4)
Application: Aggregation Bias
87(1)
Best Estimation in a Constrained Parameter Space
88(2)
Summary
90(1)
Notes
90(1)
Exercises
91(4)
Addendum: Variance of Variance Estimator
95(4)
Distributional Theory
99(26)
Introduction
99(1)
Multivariate Normal Distribution
99(4)
Chi-Square and Related Distributions
103(7)
Distribution of Quadratic Forms
110(3)
Cochran's Theorem
113(2)
Regression Models with Joint Normality
115(3)
Summary
118(1)
Notes
118(1)
Exercises
119(6)
Statistical Inference
125(32)
Introduction
125(1)
Results from Statistical Theory
125(3)
Testing the General Linear Hypothesis
128(8)
The Likelihood Ratio Test and Change in SSE
136(3)
First Principles Test and LRT
139(2)
Confidence Intervals and Multiple Comparisons
141(6)
Identifiability
147(3)
Summary
150(1)
Notes
151(1)
Exercises
151(6)
Further Topics in Testing
157(24)
Introduction
157(1)
Reparameterization
157(3)
Applying Cochran's Theorem for Sequential SS
160(9)
Orthogonal Polynomials and Contrasts
169(4)
Pure Error and the Lack of Fit Test
173(2)
Heresy: Testing Nontestable Hypotheses
175(2)
Summary
177(1)
Exercises
177(4)
Variance Components and Mixed Models
181(26)
Introduction
181(1)
Variance Components: One Way
181(5)
Variance Components: Two-Way Mixed ANOVA
186(3)
Variance Components: General Case
189(5)
Maximum Likelihood
190(2)
Restricted Maximum Likelihood (REML)
192(1)
The ANOVA Approach
193(1)
The Split Plot
194(5)
Predictions and BLUPs
199(3)
Summary
202(1)
Notes
202(1)
Exercises
203(4)
The Multivariate Linear Model
207(30)
Introduction
207(1)
The Multivariate Gauss-Markov Model
207(4)
Inference Under Normality Assumptions
211(5)
Testing
216(12)
First Principles Again
217(3)
Likelihood Ratio Test and Wilks' Lambda
220(3)
Other Test Statistics
223(1)
Power of Tests
224(4)
Repeated Measures
228(3)
Confidence Intervals
231(2)
Summary
233(1)
Notes
233(1)
Exercises
234(3)
Appendix A Review of Linear Algebra
237(32)
A.1 Notation and Fundamentals
237(2)
A.2 Rank, Column Space, and Nullspace
239(5)
A.3 Some Useful Results
244(1)
A.4 Solving Equations and Generalized Inverses
245(6)
A.5 Projecton and Idempotent Matrices
251(3)
A.6 Trace, Determinants, and Eigenproblems
254(3)
A.7 Definiteness and Factorizations
257(3)
A.8 Notes
260(1)
A.9 Exercises
261(8)
Appendix B Lagrange Multipliers
269(4)
B.1 Main Results
269(2)
B.2 Notes
271(1)
B.3 Exercises
272(1)
Bibligoraphy 273(4)
Index 277
John F. Monahan