Introduction to the Mathematical and Statistical Foundations of EconometricsThis book is intended for use in a rigorous introductory PhD level course in econometrics. |
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 |
The Multivariate Normal Distribution and Its Application | 110 |
A Proof of Theorem 5 8 | 134 |
Notations | 157 |
Dependent Laws of Large Numbers and Central Limit | 179 |
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 |
Common terms and phrases
a₁ absolutely continuous algebra Appendix arbitrary asymptotic B₁ binomial Borel sets Borel-measurable function called central limit theorem Chapter characteristic function columns corresponding countable defined Definition denoted Derive det(A diagonal elements diagonal matrix disjoint sets distribution function econometrics eigenvalues eigenvectors equal Euclidean example exists f₁ follows from Theorem function f(x gn(x hence implies independent inequality integral involved large numbers latter law of large Lebesgue measure Lemma Let Xn limn limsup linear ML estimator moment-generating function Moreover nonnegative nonsingular Note null hypothesis o-algebra orthogonal parameter permutation matrix probability measure probability space Prove Theorem random variables random vectors real function real numbers result scalar series process Similarly standard normal distribution subsets subspace spanned symmetric U₁ unit matrix vector space X₁ Y₁ Z₁ zero θεΘε θα θο σ²