| General Information | - | Schedule of Topics | - | Assignments | - | Textbook Errata |
In a nutshell, I'll plan to cover chapters 1, 2, and 5, followed by topics from chapters 6, 7, 3, and 4.
I've posted the brief outlines I use at the beginning of each class here.
| Week 1 | Tuesday August 22 |
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 24 |
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 29 |
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 31 |
Section 2.3 Convergence in law; asymptotic distribution of a sequence of random variables. |
| Week 3 | Tuesday September 5 |
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 7 |
Sections 2.5, 2.2 Examples of delta method; Slutsky's theorem(s); variance stabilizing transformations; stationarity and m-dependence. |
| Week 4 | Tuesday September 12 |
Section 2.7 Triangular arrays; Lyapunov and Lindeberg conditions for asymptotic normality; Poisson-binomial distribution. | Thursday September 14 |
Sections 2.7, 2.8 Asymptotic normality of regression estimators; stationary sequences; asymptotic normality of stationary m-dependent sequences. |
| Week 5 | Tuesday September 19 |
Section 2.8 continued Sampling from a finite population; hypergeometric distribution; Wilcoxon rank-sum statistic. | Thursday September 21 |
Section 5.1 Definitions of multivariate cdf, convergence in probability, convergence in distribution; multivariate Slutsky's theorem. |
| Week 6 | Tuesday September 26 |
Test over Chapters 1 and 2;
Sections 5.1, 5.2 The test will run from 2:25-3:25 and you may bring along a single sheet of notes (2-sided). In Sections 5.1 and 5.2, we'll cover the multivariate version of the delta method; joint distribution of uniform order statistics; bivariate normal distribution. | Thursday September 28 |
Section 5.2 More on bivariate and multivariate normal; multivariate CLT. |
| Week 7 | Tuesday October 3 |
Sections 5.2, 5.3, 5.5 Change of variables, uniform order statistics, sample correlation coefficient | Thursday October 5 |
Sections 5.4, 5.5 Pearson chi-square statistic |
| Week 8 | Tuesday October 10 |
Fall break No class. | Thursday October 12 |
Sections 5.6, 5.4 2x2 Tables, joint asymptotic distribution of quantiles |
| Week 9 | Tuesday October 17 |
Sections 3.1, 3.3 Asymptotically equivalent tests, consistent tests, asymptotic power, sample size calculations | Thursday October 19 |
Sections 3.3, 3.4 Asymptotic power of Pearson's chi-square test, efficacy, asymptotic relative efficiency |
| Week 10 | Tuesday October 24 |
Section 3.4 Power of the Wilcoxon signed rank and rank-sum tests, comparison of signed rank test with t test and sign test | Thursday October 26 |
Section 6.1 Statistical functionals, U- and V-statistics |
| Week 11 | Tuesday October 31 |
Sections 6.1, 6.2 Asymptotic normality of U- and V-statistics, Wilcoxon signed rank statistic | Thursday November 2 |
Test over Chapters 5 and 3
(with some emphasis placed on chapters 1 and 2 as well). The test will run from 2:25-3:25 and you may bring along a 2-sided sheet of notes. |
| Week 12 | Tuesday November 7 |
Sections 6.1, 6.5 Multisample U-statistics, Wilcoxon rank-sum, bootstrapping | Thursday November 9 |
Section 6.5 Bootstrapping continued |
| Week 13 | Tuesday November 14 |
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 16 |
Section 7.3 Asymptotic normality of consistent sequence of roots of likelihood equation under certain regularity conditions |
| Week 14 | Tuesday November 21 |
Sections 7.3, 7.4 Asymptotic efficiency, asymptotically efficient estimators via Newton's method | Thursday November 23 |
Thanksgiving holiday No class. |
| Week 15 | Tuesday November 28 |
Section 7.5 Fisher information, asymptotic normality of MLE, and efficient estimators via Newton's method for the multiparameter case | Thursday November 30 |
Section 7.6 Asymptotic efficiency in the multiparameter case |
| Week 16 | Tuesday December 5 |
Section 7.7 Wald, likelihood ratio, and Rao (score) tests | Thursday December 7 |
Section 7.7, recap |
| Week 17 | Monday December 11 through Friday December 15 |
Finals week. The final for this class will be Wednesday, December 13 from 6:50-8:40 pm in room 111 Thomas (NOTE: DIFFERENT ROOM!). |