## 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 |

A Uniqueness of Characteristic Functions | 61 |

A Proof of Theorem 3 12 | 83 |

A Tedious Derivations | 104 |

A Proof of Theorem 5 8 | 134 |

A Proof of the Uniform Weak Law | 164 |

C Convergence of Characteristic Functions | 174 |

A Hilbert Spaces | 199 |

Maximum Likelihood Theory | 205 |

Review of Linear Algebra | 229 |

Miscellaneous Mathematics | 283 |

A Brief Review of Complex Analysis | 298 |

Tables of Critical Values | 306 |

Dependent Laws of Large Numbers and Central Limit | 179 |

### Common terms and phrases

a e Q absolutely continuous algebra Appendix arbitrary asymptotic binomial Borel sets Borel-measurable function called central limit theorem Chapter characteristic function columns corresponding countable critical value defined Definition denoted Derive det(A diagonal elements diagonal matrix disjoint sets distribution function easy to verify econometrics eigenvalues eigenvectors equal example exists exp(i follows from Theorem function f(x hence implies inequality integral involved large numbers latter law of large Lebesgue measure Lemma Let Xn likelihood function limn limsup ML estimator moment-generating function Moreover n x n matrix n-co nonnegative nonsingular Note null hypothesis o-algebra parameter permutation matrix plim probability measure probability space Prove Theorem random variables random vectors real function real numbers result scalar series process Similarly ſº space Q standard normal distribution subsets of Q subspace spanned swapping symmetric unit matrix vector space zero