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Course schedule
| Lec |
Date |
Topic |
Material |
Exercises |
Remarks |
| 1 |
9/9 |
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 |
16/9 |
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 |
23/9 |
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 |
30/9 |
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, 2.12 |
|
| 5 |
7/10 |
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
|
14/10 |
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 |
|
|
21/10 |
-- MIDTERM EXAM -- 10:00-12:00h (+ extra
time)
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28/10 |
-- NO CLASS --
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| 7 |
4/11 |
Delta method, more examples of the delta
method
|
Book: Sec. 3.1
Syllabus: Sec. 3.1
|
3.1, 3.2, 3.3 |
|
| 8 |
11/11 |
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 |
18/11 |
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 |
25/11 |
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 |
2/12 |
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 |
9/12 |
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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-- FINAL EXAM -- (TBA)
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-- |
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-- RESIT EXAM -- (TBA)
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