Roapmap for STATS 730 Final examination, semester 2, 2021
Notes:
This roadmap aims to help students prepare, and plan, their final
examination. br>? It is recommend to always study from both the latest version of the
slides. The annotated slides are good for details that you may not
understand. However, the annotated slides may have undesired typos
that have been corrected in the latest versions of slides.
The final examination has 5 question. Questions 1& 2 are concerned
about the first half of the course. Question 3, 4 & 5 evaluate the
second half of the course.
The times given are just an estimate, times can vary dependent on
students’ strengths.
Read all the exam before you start answering. Decide an order to an-
swer your questions. Answer questions that you feel more comfortable
with, or are stronger at, first.
Supervise/manage your time carefully.
Follow the examination rules.
Question 1 [15 marks]
[Estimated time: 20 minutes]
This is concern with a specific distribution. The question has the following
items:
a) [2 marks] Question about property of such distribution.
b) [2 marks] Question about the Crame′r-Rao bound for such distribution.
(recommend to think of cases when the Cramer Rao theorem does not
hold)
c) [5 marks] Question about sufficiency for such distribution.
d) [6 marks] Question about the MLE for such distribution.
1
Question 2 [15 marks]
[Estimated time: 20 minutes]
This question has several items, asking about specific concepts, or applica-
tion of such concepts.
a) [3 marks] Question about the Delta Method
b) [4 marks] Question about Variance-stabilising transformation (answer
does not depend on previous item).
c) [5 marks] Question about the variance of MLE (Note: Recommend to
study all the different forms of finding variances for MLE, including
direct form, asymptotic form, and Fisher information). (answer does
not depend on previous items).
d) [3 marks] Question about contour lines and confidence levels. (answer
does not depend on previous items)
Question 3 [20 marks]
[Estimated time: 20 minutes]
This question is about general concepts. It has the following items
a) [5 marks] Question about properties of the EM algorithm
b) [5 marks] Question about multi-stage maximisation (or an application
of). (answer does not depend on previous items)
c) [5 marks] Question about pseudo/quasi-likelihood estimators. (answer
does not depend on previous items)
d) [5 marks] This is a short proof about properties of exponential family
(answer does not depend on previous items) (recommend to study from
the assignments for this)
Question 4 [10 marks]
[Estimated time: 15 minutes]
This question is about variance, limiting variance, and asymptotic vari-
ance of a MLE (Recommend to study from the slides and examples). It has
the following items
2
[3 marks] Find variance of the MLE
[4 marks] Find limiting variance of the MLE
[3 marks] Find the asymptotic variance of the MLE
Question 5 [20 marks]
[Estimated time: 25 minutes]
This question is about mixed models. Given that assignments did not
evaluate mixed models, I recommend to study from previous years exams,
or the current slides. You can access previous exams (for any course) via
the University library website. The question has the following items
a) [10 marks] This is about log-restricted maximum likelihood.
b) [10 marks] This is about BLUPs
End of STATS 730 Final examination Roadmap