Cover -- Title Page -- Copyright Page -- Preface -- Contents -- 1 Introduction -- 1.1 Prototype of statistical problems -- 1.2 Statistical problems and their models -- 1.3 Statistical uncertainty: inevitable controversies -- 1.4 The emergence of statistics -- 1.5 Fisher and the third way -- 1.6 Exercises -- 2 Elements of likelihood inference -- 2.1 Classical definition -- 2.2 Examples -- 2.3 Combining likelihoods -- 2.4 Likelihood ratio -- 2.5 Maximum and curvature of likelihood -- 2.6 Likelihood-based intervals -- 2.7 Standard error and Wald statistic -- 2.8 Invariance principle -- 2.9 Practical implications of invariance principle -- 2.10 Exercises -- 3 More properties of likelihood -- 3.1 Sufficiency -- 3.2 Minimal sufficiency -- 3.3 Multiparameter models -- 3.4 Profile likelihood -- 3.5 Calibration in multiparameter case -- 3.6 Exercises -- 4 Basic models and simple applications -- 4.1 Binomial or Bernoulli models -- 4.2 Binomial model with under-or overdispersion -- 4.3 Comparing two proportions -- 4.4 Poisson model -- 4.5 Poisson with overdispersion -- 4.6 Traffic deaths example -- 4.7 Aspirin data example -- 4.8 Continuous data -- 4.9 Exponential family -- 4.10 Box-Cox transformation family -- 4.11 Location-scale family -- 4.12 Exercises -- 5 Frequentist properties -- 5.1 Bias of point estimates -- 5.2 Estimating and reducing bias -- 5.3 Variability of point estimates -- 5.4 Likelihood and P-value -- 5.5 CI and coverage probability -- 5.6 Confidence density, CI and the bootstrap -- 5.7 Exact inference for Poisson model -- 5.8 Exact inference for binomial model -- 5.9 Nuisance parameters -- 5.10 Criticism of CIs -- 5.11 Exercises -- 6 Modelling relationships: regression models -- 6.1 Normal linear models -- 6.2 Logistic regression models -- 6.3 Poisson regression models -- 6.4 Nonnormal continuous regression.

6.5 Exponential family regression models -- 6.6 Deviance in GLM -- 6.7 Iterative weighted least squares -- 6.8 Box-Cox transformation family -- 6.9 Location-scale regression models -- 6.10 Exercises -- 7 Evidence and the likelihood principle* -- 7.1 Ideal inference machine? -- 7.2 Sufficiency and the likelihood principles -- 7.3 Conditionality principle and ancillarity -- 7.4 Birnbaum's theorem -- 7.5 Sequential experiments and stopping rule -- 7.6 Multiplicity -- 7.7 Questioning the likelihood principle -- 7.8 Exercises -- 8 Score function and Fisher information -- 8.1 Sampling variation of score function -- 8.2 The mean of S (θ) -- 8.3 The variance of S (θ) -- 8.4 Properties of expected Fisher information -- 8.5 Cramér-Rao lower bound -- 8.6 Minimum variance unbiased estimation -- 8.7 Multiparameter CRLB -- 8.8 Exercises -- 9 Large-sample results -- 9.1 Background results -- 9.2 Distribution of the score statistic -- 9.3 Consistency of MLE for scalar θ -- 9.4 Distribution of MLE and the Wald statistic -- 9.5 Distribution of likelihood ratio statistic -- 9.6 Observed versus expected information* -- 9.7 Proper variance of the score statistic* -- 9.8 Higher-order approximation: magic formula* -- 9.9 Multiparameter case: θ ∈ Rp -- 9.10 Examples -- 9.11 Nuisance parameters -- 9.12 χ2 goodness-of-fit tests -- 9.13 Exercises -- 10 Dealing with nuisance parameters -- 10.1 Inconsistent likelihood estimates -- 10.2 Ideal case: orthogonal parameters -- 10.3 Marginal and conditional likelihoods -- 10.4 Comparing Poisson means -- 10.5 Comparing proportions -- 10.6 Modified profile likelihood* -- 10.7 Estimated likelihood -- 10.8 Exercises -- 11 Complex data structures -- 11.1 ARMA models -- 11.2 Markov chains -- 11.3 Replicated Markov chains -- 11.4 Spatial data -- 11.5 Censored/survival data -- 11.6 Survival regression models.

11.7 Hazard regression and Cox partial likelihood -- 11.8 Poisson point processes -- 11.9 Replicated Poisson processes -- 11.10 Discrete time model for Poisson processes -- 11.11 Exercises -- 12 EM Algorithm -- 12.1 Motivation -- 12.2 General specification -- 12.3 Exponential family model -- 12.4 General properties -- 12.5 Mixture models -- 12.6 Robust estimation -- 12.7 Estimating infection pattern -- 12.8 Mixed model estimation* -- 12.9 Standard errors -- 12.10 Exercises -- 13 Robustness of likelihood specification -- 13.1 Analysis of Darwin's data -- 13.2 Distance between model and the 'truth' -- 13.3 Maximum likelihood under a wrong model -- 13.4 Large-sample properties -- 13.5 Comparing working models with the AIC -- 13.6 Deriving the AIC -- 13.7 Exercises -- 14 Estimating equations and quasi-likelihood -- 14.1 Examples -- 14.2 Computing in nonlinear cases -- 14.3 Asymptotic distribution -- 14.4 Generalized estimating equation -- 14.5 Robust estimation -- 14.6 Asymptotic Properties -- 15 Empirical likelihood -- 15.1 Profile likelihood -- 15.2 Double-bootstrap likelihood -- 15.3 BC a bootstrap likelihood -- 15.4 Exponential family model -- 15.5 General cases: M-estimation -- 15.6 Parametric versus empirical likelihood -- 15.7 Exercises -- 16 Likelihood of random parameters -- 16.1 The need to extend the likelihood -- 16.2 Statistical prediction -- 16.3 Defining extended likelihood -- 16.4 Exercises -- 17 Random and mixed effects models -- 17.1 Simple random effects models -- 17.2 Normal linear mixed models -- 17.3 Estimating genetic value from family data * -- 17.4 Joint estimation of β and b -- 17.5 Computing the variance component via and -- 17.6 Examples -- 17.7 Extension to several random effects -- 17.8 Generalized linear mixed models -- 17.9 Exact likelihood in GLMM -- 17.10 Approximate likelihood in GLMM -- 17.11 Exercises.

18 Nonparametric smoothing -- 18.1 Motivation -- 18.2 Linear mixed models approach -- 18.3 Imposing smoothness using random effects model -- 18.4 Penalized likelihood approach -- 18.5 Estimate of f given σ2 and -- 18.6 Estimating the smoothing parameter -- 18.7 Prediction intervals -- 18.8 Partial linear models -- 18.9 Smoothing nonequispaced data* -- 18.10 Non-Gaussian smoothing -- 18.11 Nonparametric density estimation -- 18.12 Nonnormal smoothness condition* -- 18.13 Exercises -- Bibliography -- Index.