Confidence intervals in generalized regression models /

Confidence intervals in generalized regression models /

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Bibliographic Details
Author / Creator:Uusipaikka, Esa.
Imprint:Boca Raton, FL : CRC Press, c2009.
Description:xxvii, 294 p. : ill. ; 25 cm. + 1 CD-ROM (4 3/4 in.).
Language:English
Series:Statistics, textbooks and monographs ; [v. 194]
Subject:
Regression analysis.
Confidence intervals.
Linear models (Mathematics)
Statistics.
Confidence intervals.
Linear models (Statistics)
Regression analysis.
Statistics.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/7255515
Hidden Bibliographic Details
ISBN:9781420060270 (alk. paper)
1420060279 (alk. paper)
Notes:Includes bibliographical references (p. 277-281) and indexes.
Table of Contents:
  • List of Tables
  • List of Figures
  • Preface
  • Introduction
  • 1. Likelihood-Based Statistical Inference
  • 1.1. Statistical evidence
  • 1.1.1. Response and its statistical model
  • 1.1.2. Sample space, parameter space, and model function
  • 1.1.3. Interest functions
  • 1.2. Statistical inference
  • 1.2.1. Evidential statements
  • 1.2.2. Uncertainties of statements
  • 1.3. Likelihood concepts and law of likelihood
  • 1.3.1. Likelihood, score, and observed information functions
  • 1.3.2. Law of likelihood and relative likelihood function
  • 1.4. Likelihood-based methods
  • 1.4.1. Likelihood region
  • 1.4.2. Uncertainty of likelihood region
  • 1.5. Profile likelihood-based confidence intervals
  • 1.5.1. Profile likelihood function
  • 1.5.2. Profile likelihood region and its uncertainty
  • 1.5.3. Profile likelihood-based confidence interval
  • 1.5.4. Calculation of profile likelihood-based confidence intervals
  • 1.5.5. Comparison with the delta method
  • 1.6. Likelihood ratio tests
  • 1.6.1. Model restricted by hypothesis
  • 1.6.2. Likelihood of the restricted model
  • 1.6.3. General likelihood ratio test statistic (LRT statistic)
  • 1.6.4. Likelihood ratio test and its observed significance level
  • 1.7. Maximum likelihood estimate
  • 1.7.1. Maximum likelihood estimate (MLE)
  • 1.7.2. Asymptotic distribution of MLE
  • 1.8. Model selection
  • 1.9. Bibliographic notes
  • 2. Generalized Regression Model
  • 2.1. Examples of regression data
  • 2.2. Definition of generalized regression model
  • 2.2.1. Response
  • 2.2.2. Distributions of the components of response
  • 2.2.3. Regression function and regression parameter
  • 2.2.4. Regressors and model matrix (matrices)
  • 2.2.5. Example
  • 2.3. Special cases of GRM
  • 2.3.1. Assumptions on parts of GRM
  • 2.3.2. Various special GRMs
  • 2.4. Likelihood inference
  • 2.5. MLE with iterative reweighted least squares
  • 2.6. Model checking
  • 2.7. Bibliographic notes
  • 3. General Linear Model
  • 3.1. Definition of the general linear model
  • 3.2. Estimate of regression coefficients
  • 3.2.1. Least squares estimate (LSE)
  • 3.2.2. Maximum likelihood estimate (MLE)
  • 3.3. Test of linear hypotheses
  • 3.4. Confidence regions and intervals
  • 3.4.1. Joint confidence regions for finite sets of linear combinations
  • 3.4.2. Separate confidence intervals for linear combinations
  • 3.5. Model checking
  • 3.6. Bibliographic notes
  • 4. Nonlinear Regression Model
  • 4.1. Definition of nonlinear regression model
  • 4.2. Estimate of regression parameters
  • 4.2.1. Least squares estimate (LSE) of regression parameters
  • 4.2.2. Maximum likelihood estimate (MLE)
  • 4.3. Approximate distribution of LRT statistic
  • 4.4. Profile likelihood-basec confidence region
  • 4.5. Profile likelihood-based confidence interval
  • 4.6. LRT for a hypothesis on finite set of functions
  • 4.7. Model checking
  • 4.8. Bibliographic notes
  • 5. Generalized Linear Model
  • 5.1. Definition of generalized linear model
  • 5.1.1. Distribution, linear predictor, and link function
  • 5.1.2. Examples of distributions generating generalized linear models
  • 5.2. MLE of regression coefficients
  • 5.2.1. MLE
  • 5.2.2. Newton-Raphson and Fisher-scoring
  • 5.3. Bibliographic notes
  • 6. Binomial and Logistic Regression Model
  • 6.1. Data
  • 6.2. Binomial distribution
  • 6.3. Link functions
  • 6.3.1. Unparametrized link functions
  • 6.3.2. Parametrized link functions
  • 6.4. Likelihood inference
  • 6.4.1. Likelihood function of binomial data
  • 6.4.2. Estimates of parameters
  • 6.4.3. Likelihood ratio statistic or deviance function
  • 6.4.4. Distribution of deviance
  • 6.4.5. Model checking
  • 6.5. Logistic regression model
  • 6.6. Models with other link functions
  • 6.7. Nonlinear binomial regression model
  • 6.8. Bibliographic notes
  • 7. Poisson Regression Model
  • 7.1. Data
  • 7.2. Poisson distribution
  • 7.3. Link functions
  • 7.3.1. Unparametrized link functions
  • 7.3.2. Parametrized link functions
  • 7.4. Likelihood inference
  • 7.4.1. Likelihood function of Poisson data
  • 7.4.2. Estimates of parameters
  • 7.4.3. Likelihood ratio statistic or deviance function
  • 7.4.4. Distribution of deviance
  • 7.4.5. Model checking
  • 7.5. Log-linear model
  • 7.6. Bibliographic notes
  • 8. Multinomial Regression Model
  • 8.1. Data
  • 8.2. Multinomial distribution
  • 8.3. Likelihood function
  • 8.4. Logistic multinomial regression model
  • 8.5. Proportional odds regression model
  • 8.6. Bibliographic notes
  • 9. Other Generalized Linear Regressions Models
  • 9.1. Negative binomial regression model
  • 9.1.1. Data
  • 9.1.2. Negative binomial distribution
  • 9.1.3. Likelihood inference
  • 9.1.4. Negative binomial logistic regression model
  • 9.2. Gamma regression model
  • 9.2.1. Data
  • 9.2.2. Gamma distribution
  • 9.2.3. Link function
  • 9.2.4. Likelihood inference
  • 9.2.5. Model checking
  • 10. Other Generalized Regression Models
  • 10.1. Weighted general linear model
  • 10.1.1. Model
  • 10.1.2. Weighted linear regression model as GRM
  • 10.2. Weighted nonlinear regression model
  • 10.2.1. Model
  • 10.2.2. Weighted nonlinear regression model as GRM
  • 10.3. Quality design or Taguchi model
  • 10.4. Lifetime regression model
  • 10.5. Cox regression model
  • 10.6. Bibliographic notes
  • A. Datasets
  • B. Notation Used for Statistical Models
  • References
  • Data Index
  • Author Index
  • Subject Index
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