| Week 1 | Tuesday August 21 |
Sections 1.1, 1.2, 1.3, 1.4 Review of idea of limit, with emphasis on the rate of convergence to a limit; asymptotic equivalence; embedding sequences and the binomial probability example; some examples of and results about infinite series; order relations and notation. | Thursday August 23 |
Sections 1.4, 1.5, 1.6 Examples of different types of growth; review of definition of continuity; review of cumulative distribution function (cdf) properties and continuity points. |
| Week 2 | Tuesday August 28 |
Sections 2.1, 2.2 Convergence in probability; Chebyshev's inequality and the WLLN; consistency; estimation of a common mean and simple linear regression estimates. | Thursday August 30 |
Section 2.3 Convergence in law; asymptotic distribution of a sequence of random variables. |
| Week 3 | Tuesday September 4 |
Sections 2.3, 2.6, 2.4, 2.5 Bounded in probability sequences; uniform convergence; central limit theorem (iid form); delta method and Taylor's theorem. | Thursday September 6 |
Sections 2.5, 2.2 Examples of delta method; Slutsky's theorem(s); variance stabilizing transformations; stationarity and m-dependence. |
| Week 4 | Tuesday September 11 |
Section 2.7 Triangular arrays; Lyapunov and Lindeberg conditions for asymptotic normality; Poisson-binomial distribution. | Thursday September 13 |
Section 2.7 continued Asymptotic normality of regression estimators; stationary sequences; asymptotic normality of stationary m-dependent sequences. |
| Week 5 | Tuesday September 18 |
Section 2.7 | Thursday September 20 |
Sections 2.7, 2.8 |
| Week 6 | Tuesday September 25 |
Test over Chapters 1 and 2 The test will run from 11:15-12:30 and you may bring along a single sheet of notes (2-sided). | Thursday September 27 |
Section 2.8 Central limit theorem for stationary m-dependent sequences, stationary autoregressive processes. |
| Week 7 | Tuesday October 2 |
Section 5.1 Multivariate extensions of univariate concepts: Limits, cdfs, convergence in probability and distribution, Slutsky's theorem, delta method; distribution of uniform sample range. Change of variables, uniform order statistics, sample correlation coefficient | Thursday October 4 |
Sections 5.2, 5.4 Multivariate Taylor's theorem, multivariate normal distribution, multivariate central limit theorem |
| Week 8 | Tuesday October 9 |
Fall break No class. | Thursday October 11 |
Section 5.4 Sample correlation coefficient |
| Week 9 | Tuesday October 16 |
Sections 5.4, 5.5, 5.6 Pearson chi-square statistic, odds ratios for 2x2 tables | Thursday October 18 |
Sections 3.1, 3.3 Asymptotically equivalent tests, consistent tests, asymptotic power |
| Week 10 | Tuesday October 23 |
Sections 3.3, 3.4 Asymptotic power of Pearson's chi-square test, efficacy, asymptotic relative efficiency, power of the Wilcoxon signed rank and rank-sum tests, comparison of signed rank test with t test and sign test | Thursday October 25 |
Sections 3.3, 3.4 Asymptotic relative efficiency of signed rank, t-test, sign test |
| Week 11 | Tuesday October 30 |
Sections 6.1, 6.2 Statistical functionals, Asymptotic normality of U- and V-statistics, Wilcoxon signed rank statistic | Thursday November 1 |
Sections 6.1, 6.5 Multisample U-statistics, Wilcoxon rank-sum, bootstrapping |
| Week 12 | Tuesday November 6 |
Test over Chapters 5 and 3
(with some emphasis placed on chapters 1 and 2 as well). The test will run from 11:15-12:30 and you may bring along a 2-sided sheet of notes. | Thursday November 8 |
Section 6.5 Bootstrapping continued |
| Week 13 | Tuesday November 13 |
Sections 7.1, 7.2 Consistency of MLE (and related complications), existence of consistent sequence of roots of likelihood equation, review of Fisher information | Thursday November 15 |
Section 7.3 Asymptotic normality of consistent sequence of roots of likelihood equation under certain regularity conditions |
| Week 14 | Tuesday November 20 |
Sections 7.3, 7.4 Asymptotic efficiency, asymptotically efficient estimators via Newton's method | Thursday November 22 |
Thanksgiving holiday No class. |
| Week 15 | Tuesday November 27 |
Section 7.5 Fisher information, asymptotic normality of MLE, and efficient estimators via Newton's method for the multiparameter case | Thursday November 29 |
Section 7.6 Asymptotic efficiency in the multiparameter case |
| Week 16 | Tuesday December 4 |
Section 7.7 Wald, likelihood ratio, and Rao (score) tests | Thursday December 6 |
Section 7.7, recap |
| Week 17 | Monday December 10 through Friday December 14 |
Finals week. The final for this class will be Thursday, December 13 from 4:40-6:30 pm in room 305 Wagner. |