## Introduction to the Mathematical and Statistical Foundations of EconometricsThis book is intended for use in a rigorous introductory PhD level course in econometrics. |

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### Contents

Probability and Measure | 1 |

A Common Structure of the Proofs of Theorems | 32 |

Conditional Expectations | 66 |

Distributions and Transformations | 86 |

The Multivariate Normal Distribution and Its Application | 110 |

Modes of Convergence | 137 |

Dependent Laws of Large Numbers and Central Limit | 179 |

Maximum Likelihood Theory | 205 |

Review of Linear Algebra | 229 |

Matrix | 248 |

Matrices | 256 |

Miscellaneous Mathematics | 283 |

A Brief Review of Complex Analysis | 298 |

Tables of Critical Values | 306 |

### Common terms and phrases

algebra Appendix applies arbitrary assume Borel sets Borel-measurable bounded called Chapter characteristic function choose collection columns components condition Consequently consider consistent containing continuous convergence corresponding countable defined Definition denoted density dependent Derive determinant diagonal disjoint distribution function easy econometrics eigenvalues elementary elements equal estimator example Exercise exists expectation Figure finite follows follows from Theorem given hence holds hypothesis implies independent inequality integral interval involved large numbers latter Lebesgue Lemma limit linear matrix mean value theorem Moreover nonsingular normal distribution Note null o-algebra observe orthogonal orthogonal matrix parameter particular permutation positive probability measure Proof Prove random variables random vectors replacement respectively result sample satisfying sequence Similarly space spanned square statistical subsets symmetric symmetric matrix takes true union unique unit variance verify zero