## Elements of Modern Asymptotic Theory with Statistical Applications |

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### Contents

Preface | 8 |

Random variables and distributions in statistics | 19 |

Likelihood and associated concepts | 106 |

Maximum likelihood and asymptotic theory | 128 |

Metric spaces and stochastic processes | 155 |

Brownian motion and weak convergence | 171 |

Applications of weak convergence | 193 |

Dependent random variables and mixing | 215 |

Dependent sequences and martingales | 238 |

255 | |

262 | |

### Common terms and phrases

applies approach argument assumed assumption asymptotic bounded Brownian motion called Chapter condition consider consistent constant constructed context continuous convergence convergence in probability course defined definition density dependent derivative difference discussion distribution function element equal established estimator evaluated Example exist expectation expression fact Figure finite follows further given gives Hence holds hypothesis implies important independent infinite integral interest interval introduced known limit mapping martingale matrix mean measure metric mixing moments natural necessary normal Note null o-field observed parameter possible probability problem properties quantity random variables reason respect result sample satisfy score seen sequence shown shows space squares standardised stationary statistic stochastic structure term Theorem theory tion true usual valid variance vector weak WLLN zero