## Elements of Modern Asymptotic Theory with Statistical Applications |

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### Contents

Probability and measure | 1 |

Concepts of asymptotic convergence | 48 |

1 | |

8 | 103 |

4 | 107 |

7 | 113 |

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 | |

### Common terms and phrases

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