## Statistical Inference Based on the likelihoodThe Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood. Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data. |

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### Contents

Likelihood | 17 |

Maximum likelihood estimation | 51 |

Hypothesis testing | 105 |

Linear models | 163 |

Generalized linear models | 223 |

Complements of probability theory | 265 |

Main abbreviations and symbols | 313 |

323 | |

Author index | 329 |

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### Common terms and phrases

algorithm analysis approximation asymptotic distribution binomial called components computed condition confidence interval consider constant corresponding criterion defined denote density function depend on 9 distribution function elements equal equivalent error estimate Example exists explanatory variables exponential family expression fact Figure frequency gamma gamma distribution given hence implies independent instance large number likelihood equations likelihood function likelihood principle linear models log-likelihood matrix mean value method minimal sufficient statistic multinomial multinomial distribution non-centrality normal null hypothesis observed obtain order statistics p-value pivotal quantity plot Poisson population probability distribution problem properties quantity random variable ratio relationship relevant residuals response variable s r s sample space sample value sequence significance level specific statistical model sufficient statistic Suppose Table term test procedure test statistic Theorem theory tion transformation treatment variance vector write