## Maximum Likelihood Estimation and Inference: With Examples in R, SAS and ADMBThis book takes a fresh look at the popular and well-established method of maximum likelihood for statistical estimation and inference. It begins with an intuitive introduction to the concepts and background of likelihood, and moves through to the latest developments in maximum likelihood methodology, including general latent variable models and new material for the practical implementation of integrated likelihood using the free ADMB software. Fundamental issues of statistical inference are also examined, with a presentation of some of the philosophical debates underlying the choice of statistical paradigm. Key features: - Provides an accessible introduction to pragmatic maximum likelihood modelling.
- Covers more advanced topics, including general forms of latent variable models (including non-linear and non-normal mixed-effects and state-space models) and the use of maximum likelihood variants, such as estimating equations, conditional likelihood, restricted likelihood and integrated likelihood.
- Adopts a practical approach, with a focus on providing the relevant tools required by researchers and practitioners who collect and analyze real data.
- Presents numerous examples and case studies across a wide range of applications including medicine, biology and ecology.
- Features applications from a range of disciplines, with implementation in R, SAS and/or ADMB.
- Provides all program code and software extensions on a supporting website.
- Confines supporting theory to the final chapters to maintain a readable and pragmatic focus of the preceding chapters.
This book is not just an accessible and practical text about maximum likelihood, it is a comprehensive guide to modern maximum likelihood estimation and inference. It will be of interest to readers of all levels, from novice to expert. It will be of great benefit to researchers, and to students of statistics from senior undergraduate to graduate level. For use as a course text, exercises are provided at the end of each chapter. |

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### Contents

Hypothesis tests and confidence intervals or regions | |

What you really need to know | |

Maximizing the likelihood | |

Some widely used applications of maximum | |

Generalized linear models and extensions | |

Dispersed Counts in | |

CramérRao inequality and Fisher information | |

Asymptotic theory and approximate normality | |

Tools of the trade | |

Fundamental paradigms and principles | |

Miscellanea | |

Partial solutions to selected exercises | |

Bibliography | |

Index | |

### Common terms and phrases

ADMB algorithm approximate normality assumed asymptotic Bayesian Bernoulli binomial model bootstrap calculation Chapter clinic conditional likelihood confidence interval convergence delta method density function derivative deviance distribution function equivalent evaluated example Exercise expected Fisher information experiment exponential family Figure frequentist GLMM hence implemented inference Laplace approximation latent variable let denote likelihood equation likelihood function likelihood principle likelihood ratio confidence likelihood ratio test linear model log-likelihood log-likelihood function logistic LRT statistic M-estimator macro maximization maximum likelihood mean and variance mixture model ML estimator multinomial negative binomial normal distribution notation null hypothesis observed obtained optimization p-value parameter space parameter value parameterization Plkhci Poisson model prediction probability PROC NLMIXED profile likelihood proportion quasi-likelihood random effect random variable ratio confidence interval REML residual saturated model Section simulated specified standard errors theorem unbiased estimator variance matrix Wald test Wald test statistic zero