Uusipaikka Confidence Intervals in Generalized Regression Models

Erscheinungsjahr 2008
ISBN: 978-1-4200-6038-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 328 Seiten

Reihe: Statistics: A Series of Textbooks and Monographs

A Cohesive Approach to Regression Models Confidence Intervals in Generalized Regression Models introduces a unified representation—the generalized regression model (GRM)—of various types of regression models. It also uses a likelihood-based approach for performing statistical inference from statistical evidence consisting of data and its statistical model. Provides a Large Collection of Models The book encompasses a number of different regression models, from very simple to more complex ones. It covers the general linear model (GLM), nonlinear regression model, generalized linear model (GLIM), logistic regression model, Poisson regression model, multinomial regression model, and Cox regression model. The author also explains methods of constructing confidence regions, profile likelihood-based confidence intervals, and likelihood ratio tests. Uses Statistical Inference Package to Make Inferences on Real-Valued Parameter Functions Offering software that helps with statistical analyses, this book focuses on producing statistical inferences for data modeled by GRMs. It contains numerical and graphical results while providing the code online.

Zielgruppe

Advanced undergraduate and graduate students and researchers in statistics.

Autoren/Hrsg.

Uusipaikka, Esa

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Introduction
Likelihood-Based Statistical Inference
Statistical evidence
Statistical inference
Likelihood concepts and law of likelihood
Likelihood-based methods
Profile likelihood-based confidence intervals
Likelihood ratio tests (LRTs)
Maximum likelihood estimate (MLE)
Model selection
Generalized Regression Model
Examples of regression data
Definition of generalized regression models (GRMs)
Special cases of GRM
Likelihood inference
MLE with iterative reweighted least squares
Model checking
General Linear Model
Definition of the general linear model (GLM)
Estimate of regression coefficients
Test of linear hypotheses
Confidence regions and intervals
Model checking
Nonlinear Regression Model
Definition of the nonlinear regression model
Estimate of regression parameters
Approximate distribution of LRT statistic
Profile likelihood-based confidence region
Profile likelihood-based confidence interval
LRT for a hypothesis on finite set of functions
Model checking
Generalized Linear Model
Definition of generalized linear model (GLIM)
MLE of regression coefficients
Binomial and Logistic Regression Models
Data
Binomial distribution
Link functions
Likelihood inference
Logistic regression model
Models with other link functions
Nonlinear binomial regression model
Poisson Regression Model
Data
Poisson distribution
Link functions
Likelihood inference
Log-linear model
Multinomial Regression
Data
Multinomial distribution
Likelihood function
Logistic multinomial regression model
Proportional odds regression model
Other Generalized Linear Regressions Models
Negative binomial regression model
Gamma regression model
Other Generalized Regression Models
Weighted GLM
Weighted nonlinear regression model
Quality design or Taguchi model
Lifetime regression model
Cox regression model
Appendix A: Data Sets
Appendix B: Notation Used for Statistical Models
Bibliographic notes appear at the end of each chapter.