# Statistics 597A Asymptotic Tools Fall 2001

## Tentative Schedule of Topics

 General Information - Schedule of Topics - Assignments - Textbook Errata

We may deviate from this schedule, though it's a pretty good sketch of what we'll cover. In a nutshell, I'll plan to cover chapters 1, 2, and 5, followed by topics from chapters 6, 7, 3, and 4 (in Lehmann's book).

 Week 1 TuesdayAugust 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. ThursdayAugust 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. Splus code seen in class Week 2 TuesdayAugust 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. ThursdayAugust 30 Section 2.3 Convergence in law; asymptotic distribution of a sequence of random variables. Week 3 TuesdaySeptember 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. ThursdaySeptember 6 Sections 2.5, 2.2 Examples of delta method; Slutsky's theorem(s); variance stabilizing transformations; stationarity and m-dependence. Splus code seen in class Week 4 TuesdaySeptember 11 Section 2.7 Triangular arrays; Lyapunov and Lindeberg conditions for asymptotic normality; Poisson-binomial distribution. ThursdaySeptember 13 Section 2.7 continued Asymptotic normality of regression estimators; stationary sequences; asymptotic normality of stationary m-dependent sequences. Week 5 TuesdaySeptember 18 Section 2.7 ThursdaySeptember 20 Sections 2.7, 2.8 Week 6 TuesdaySeptember 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). ThursdaySeptember 27 Section 2.8 Central limit theorem for stationary m-dependent sequences, stationary autoregressive processes. Splus code seen in class Week 7 TuesdayOctober 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 ThursdayOctober 4 Sections 5.2, 5.4 Multivariate Taylor's theorem, multivariate normal distribution, multivariate central limit theorem Week 8 TuesdayOctober 9 Fall break No class. ThursdayOctober 11 Section 5.4 Sample correlation coefficient Mathematica code seen in class Week 9 TuesdayOctober 16 Sections 5.4, 5.5, 5.6 Pearson chi-square statistic, odds ratios for 2x2 tables ThursdayOctober 18 Sections 3.1, 3.3 Asymptotically equivalent tests, consistent tests, asymptotic power Week 10 TuesdayOctober 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 ThursdayOctober 25 Sections 3.3, 3.4 Asymptotic relative efficiency of signed rank, t-test, sign test Mathematica code see in class regarding Problem 3.4.20(ii) and covariance matrix delta method. Week 11 TuesdayOctober 30 Sections 6.1, 6.2 Statistical functionals, Asymptotic normality of U- and V-statistics, Wilcoxon signed rank statistic Splus code seen in class ThursdayNovember 1 Sections 6.1, 6.5 Multisample U-statistics, Wilcoxon rank-sum, bootstrapping Week 12 TuesdayNovember 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. ThursdayNovember 8 Section 6.5 Bootstrapping continued Week 13 TuesdayNovember 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 ThursdayNovember 15 Section 7.3 Asymptotic normality of consistent sequence of roots of likelihood equation under certain regularity conditions Week 14 TuesdayNovember 20 Sections 7.3, 7.4 Asymptotic efficiency, asymptotically efficient estimators via Newton's method ThursdayNovember 22 Thanksgiving holiday No class. Week 15 TuesdayNovember 27 Section 7.5 Fisher information, asymptotic normality of MLE, and efficient estimators via Newton's method for the multiparameter case ThursdayNovember 29 Section 7.6 Asymptotic efficiency in the multiparameter case Week 16 TuesdayDecember 4 Section 7.7 Wald, likelihood ratio, and Rao (score) tests ThursdayDecember 6 Section 7.7, recap Week 17 MondayDecember 10 throughFridayDecember 14 Finals week. The final for this class will be Thursday, December 13 from 4:40-6:30 pm in room 305 Wagner.

Last updated: August 14, 2001
dhunter@stat.psu.edu