|
Course schedule (subject to change)
| Lec |
Date |
Topic |
Material |
Exercises |
Remarks |
| 1 |
13/9 |
Modes of stochastic convergence, Portmanteau
lemma, continuous mapping theorem |
Book: Ch. 1, Sec. 2.1
(up to and including thm 2.3)
Syllabus: Sec. 1.1 (up to and including thm 1.7) |
1.1, 1.2, 1.3(i), 1.4,
1.10, 1.15 |
|
| 2 |
20/9 |
Tightness, Prohorov's theorem, Helly's lemma |
Book: Sec. 2.1 (up to and including ex 2.6)
Syllabus: Sec. 1.1 (up to and including ex 1.10)
|
1.7, 1.12, 1.23, 1.25, 1.17, 1.19, 1.21 |
|
| 3 |
27/9 |
Relations between modes of convergence, Slutsky,
stochastic O() and o() |
Book: Sec. 2.1 (rest) and sec. 2.2
Syllabus: Sec. 1.1 (rest) |
1.11, 1.31, 1.32, 1.24, 1.29(i) |
|
| 4 |
4/10 |
Multivariate random variables, marginal normality,
covariance matrix with properties, definition
multivariate normal distribution |
Syllabus: Sec. 2.1, 2.2 (up to and including lemma
2.3) |
1.20, 2.1, 2.2, 2.5, 2.6, 2.7, 2.9 (correct: the
second 'independent' is 'uncorrelated'), 2.12 |
|
| 5 |
11/10 |
Multivariate normal distribution and
one-dimensional projections, normality under linear
mapping, multivariate central limit theorem,
distribution of squared norm of a normally
distributed vector, Chi-squared distribution |
Syllabus: Sec. 2.2 (rest), Sec. 2.3, 2.4 |
2.3, 2.8, 2.13, 2.14, 2.10, 2.15, 2.16 |
|
| 6 |
18/10 |
Asymptotic distribution of Cn-statistic in
multinomial testing, example of the Delta method |
Syllabus: Sec. 2.5, Sec. 3.1 (up to thm 3.1) |
2.17, 2.18, 2.19, 2.20, 2.23(i), 3.1 |
|
|
25/10 |
MIDTERM EXAM
|
|
|
|
| 7 |
1/11 |
Delta method, more examples of the delta method |
Book: Sec. 3.1
Syllabus: Sec. 3.1
|
3.1, 3.2, 3.3 |
|
| 8 |
8/11 |
Variance stabilising transformations, method of
moments, asymptotic distribution of moment
estimator, setting for M- and Z-estimation |
Book: Sec. 3.2, 4.1
Syllabus: Sec, 3.2, 3.3 |
3.11, 3.12, 3.15 |
|
| 9 |
15/11 |
M-estimators (general definition, MLE,
M-estimators of location), Z-estimators |
Book: Sec. 5.1
Syllabus: Introductory remarks of Ch. 4 (up to sec.
4.1) |
3.14, 3.16, 3.18 |
|
| 10 |
22/11 |
Consistency of M-estimators and of Z-estimators,
Glivenko-Cantelli property, alternative consistency
conditions for Z-estimators, asymptotic normality
(property), an introduction to asymptotic normality |
Book: Sec. 5.2 (up to subsec. 5.2.1)
Syllabus: Sec. 4.1 |
3.19, 3.20
|
|
| 11 |
29/11 |
Asymptotic normality again, asymptotic normality
of Z-estimators, asymptotic relative efficiency |
Book: Sec. 5.3
Syllabus: Sec. 4.2 |
4.1, 4.2, 4.4, 4.10, 4.11, 4.17 |
|
| 12 |
6/12 |
Maximum likelihood estimation, Fisher information
and Cramer-Rao, asymptotic optimality, model
mis-specification |
Book: Sec. 5.5
Syllabus: Sec. 4.3
|
4.18, 4,21, 4.22, 4.19, 4,20, 4.23
|
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