Cover -- Dedication Page -- Title Page -- Copyright Page -- Contents -- Preface -- Notation and Acronyms -- Chapter 1. Exponential Families -- 1.1. Definition -- 1.2. Mean, variance, and variance function -- 1.3. Examples of exponential families -- 1.4. Maximum likelihood estimation -- 1.5. Technical appendix -- 1.5.1. Some useful results from probability -- 1.5.2. Negative binomial distribution and Poisson-gamma mixtures -- 1.6. Exercises -- Chapter 2. From Linear Models to GLMs -- 2.1. Reminders on the linear model -- 2.1.1. Matrix form of the linear model -- 2.1.2. Some examples of linear models -- 2.1.3. Least-squares approximation -- 2.1.4. Asymptotics of the LSE -- 2.1.5. Linear Gaussian model -- 2.2. Three components of a generalized linear model -- 2.2.1. The random component -- 2.2.2. The linear predictor -- 2.2.3. The link function -- 2.3. Estimation in generalized linear models -- 2.3.1. Maximum likelihood -- 2.3.2. Asymptotic properties and inference -- 2.3.3. Estimating the dispersion parameter -- 2.4. Some examples -- 2.4.1. Logistic regression model -- 2.4.2. Poisson regression model -- 2.4.3. Gamma regression model -- 2.5. Generalized linear models in R: Poisson regression example -- 2.5.1. Confidence intervals and hypothesis tests -- 2.5.2. AIC and BIC, variable selection -- 2.5.3. Prediction, confidence intervals for a prediction -- 2.6. Technical appendix -- 2.6.1. Some probability distributions -- 2.6.2. Cochran's theorem -- 2.7. Exercises -- Chapter 3. Censored and Missing Data in GLMs -- 3.1. Censored data -- 3.1.1. Introduction -- 3.1.2. Poisson regression with a right-censored response -- 3.1.3. Gamma regression with a right-censored response -- 3.2. Missing data problems -- 3.2.1. Introduction -- 3.2.2. Missing data typology -- 3.2.3. Methods for treating missing data -- 3.2.4. A missing data problem in the Poisson model.

3.2.5. A missing data problem in the gamma regression model -- 3.3. Technical appendix -- 3.3.1. Two lemmas -- 3.3.2. Proof of theorem 3.3 -- 3.3.3. Proof of theorem 3.4 -- 3.3.4. Proof of theorem 3.5 -- 3.3.5. Proof of theorem 3.6 -- 3.3.6. Elements of empirical processes -- 3.4. Exercises -- Chapter 4. Zero-Inflated Models -- 4.1. Introduction -- 4.1.1. Overdispersion -- 4.1.2. Excess of zeros -- 4.2. Zero-inflated Poisson models and extensions -- 4.2.1. The zero-inflated Poisson model -- 4.2.2. Semi-parametric ZIP models -- 4.2.3. Zero-inflated generalized Poisson model -- 4.2.4. A zero-inflation test -- 4.3. Zero-inflated negative binomial model -- 4.3.1. Negative binomial model -- 4.3.2. ZINB model -- 4.3.3. The ZIP model versus the ZINB model -- 4.4. Zero-inflated binomial model -- 4.5. Censored and missing data: examples of problems -- 4.5.1. Censored ZIP model -- 4.5.2. Missing covariables in the ZIB model -- 4.5.3. Missing covariables in the ZIP model -- 4.6. Marginal zero-inflated models -- 4.6.1. Introduction -- 4.6.2. MZIP and MZINB models -- 4.7. Exercises -- References -- Index -- Other titles from ISTE in Mathematics and Statistics -- EULA.