## 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

additional analysis applied approximation associated assumed asymptotic called Chapter components computed condition consider constant corresponding defined definition denote density function depends discussion distribution effect elements equal equations equivalent error estimate Example exists expected exponential expression fact factor Figure frequency given gives hence holds implies independent instance interest interval introduced leading likelihood likelihood function log-likelihood matrix mean value method minimal namely normal Notice null hypothesis observed obtain parameter plot population positive possible practical present probability problem properties quantity random variable reasons region regression relationship Remark represents respect sample satisfied selection sequence shows similar simple situation solution space specific squares sufficient statistic Suppose Table taking term test statistic Theorem theory tion transformation treatment variance vector write