## Essentials of Statistical InferenceThis textbook presents the concepts and results underlying the Bayesian, frequentist, and Fisherian approaches to statistical inference, with particular emphasis on the contrasts between them. Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, it covers basic mathematical theory as well as more advanced material, including such contemporary topics as Bayesian computation, higher-order likelihood theory, predictive inference, bootstrap methods, and conditional inference. |

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### Contents

Introduction | 1 |

1 | 22 |

3 | 32 |

6 | 39 |

8 | 48 |

3 | 65 |

Special models | 81 |

Sufficiency and completeness | 90 |

Twosided tests and conditional inference | 98 |

Likelihood theory | 120 |

Higherorder theory | 140 |

Predictive inference | 169 |

Bootstrap methods | 190 |

Bibliography | 218 |

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### Common terms and phrases

analysis applied approach approximation assume asymptotic Bayes Bayesian bootstrap calculate called Chapter conditional conditional distribution confidence set consider constant construct continuous corresponding coverage decision rule defined definition denotes density depend derivatives discussion distribution error exact exactly example exists expansion expected exponential family expression factor Figure fixed follows function given gives H₁ hypothesis ideas identically distributed independent inference integration interest interval known lead likelihood ratio log-likelihood loss maximum likelihood estimator mean methods minimal sufficient minimax natural Note nuisance parameter observed obtained parameter particular possible posterior practice predictive principle prior probability problem procedure properties random variables respect result risk root sample Show simple situation specific standard statistic sufficient statistic Suppose Theorem theory true unbiased unknown variance write