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MATH5905

Statistical Inference
Administrative Contacts
Please visit the School of Mathematics and Statistics website for a range of information on School
Policies, Forms and Help for Students.

For information on Courses, please go to “Current Students” and either Undergraduate and/or
Postgraduate”, Course Homepage” for information on all course offerings,

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posted regularly for your information here.

If you cannot find the answer to your queries on the web you are welcome to contact the Student
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By phone: 9385 7053
Should we need to contact you, we will use your official UNSW email address of in the first
instance. It is your responsibility to regularly check your university email account. Please state
your student number in all emails.

Course Information

Excluded: MATH3811, MATH3911

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Course Aims

The aim of the course is to introduce the main ideas and principles behind the parametric and
nonparametric inference procedures. Both frequentist and Bayesian perspective will be discussed.
Estimation, confidence set construction and hypothesis testing are discussed within decision
theoretic framework. Both finite sample optimality and asymptotic optimality will be defined and
discussed.

Computationally intensive methods such as bootstrap are discussed and are compared to
asymptotic approximations such as Edgeworth expansions and saddle point method. Students will
learn how to determine appropriate inference procedure and to draw inferences using the chosen
procedure. Time permitting, applications in Statistical Financial Engineering will shortly be
discussed.

Course Description
This course presents General interference theory based on maximum likelihood and on Bayes
methods is reviewed. Estimation, confidence set construction and hypothesis testing are
discussed within decision-theoretic framework. Computationally intensive methods such as
bootstrap are discussed and are compared to asymptotic approximations such as saddle point
and empirical likelihood.

Assessment and Deadlines

Assessment Week Weighting
%
Due date if
applicable
CLO’s
Assignment 1 Week 4 10% 12 March CLO1, CLO2
Midterm Test Week 7 20% 30 March CLO3, CLO4
Assignment 2 Week 9 10% 16 April CLO5, CLO6
Final Exam Exam period 60% ALL CLO’s

Late Submission of Assessment Tasks
No late submissions will be accepted. (Where "late" in this context means after any extensions
granted for Special Consideration or Equitable Learning Provisions.)

Course Learning Outcomes (CLO)

1. Show how Statistical Inference arises from the first principles of Probability Theory.
2. Understand the fundamental principles of inference: sufficiency, likelihood, ancillarity,
equivariance.
3. Comprehend the concepts of finite-sample and asymptotic efficiency of
Inference Procedure.
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4. Demonstrate mastery of the parametric and non-parametric delta method,
asymptotic normality, Edgeworth expansions and saddle point method.
5. Estimate key population parameters of interest, to test hypotheses about them and to
construct confidence regions.
6. Use in practice the parametric, nonparametric, Bayes and robust inference.
7. Use computer packages to generate output for the most common Inference Procedures
and for computer-intensive calculations such as bootstrapping and robust estimation.

Course Schedule
The course will include material taken from some of the following topics. This is should only serve
as a guide as it is not an extensive list of the material to be covered and the timings are
approximate. The course content is ultimately defined by the material covered in lectures.


Weeks Topic Reading (if
applicable)
1 Revision. The general inference problem as a decision-theoretic
problem.


Refer to
Moodle
Lecture notes
2 Bayes and minimax decision rules. Principles of data reduction and
inference.
3 Classical estimation theory. Methods for finding estimators.
Information and likelihood.
4 Expected and observed Fisher information matrices. Cramer-Rao
bound. Uniform minimum variance unbiased estimators.
5 Likelihood inference. Estimating statistical functionals. Asymptotic
properties of estimators.
7 Order statistics. Hypothesis testing. Neyman-Pearson theory.
8 Generalized Likelihood Ratio Tests. Higher order asymptotics.
9 Edgeworth expansions. Saddlepoint approximations. Laplace's
method.
10 An introduction to the bootstrap as a computationally intensive
method. Robustness.

From the textbooks, the recommended text by Casella and Berger (2001) will be most useful. The
remaining texts complement the lecture notes and cover different aspects of the course. Lecture
notes will be provided regularly, before the start of each week.

The books of Young and Smith (2005) and A.W. van der Vaart (1998) are a bit more advanced but
contain important material and will be used for some more specialized topics. The textbook
DasGupta, A. (2008) is an encyclopaedic book covering both classical and modern topics of
inference. It also contains many examples.

Moodle
Log in to Moodle to find announcements, general information, notes, lecture slide, classroom tutorial
and assessments etc.

School and UNSW Policies
The School of Mathematics and Statistics has adopted a number of policies relating to enrolment,
attendance, assessment, plagiarism, cheating, special consideration etc. These are in addition to
the Policies of The University of New South Wales. Individual courses may also adopt other
policies in addition to or replacing some of the School ones. These will be clearly notified in the
Course Initial Handout and on the Course Home Pages on the Maths Stats web site.


The School of Mathematics and Statistics will assume that all its students have read and
understood the School policies on the above pages and any individual course policies on the
Course Initial Handout and Course Home Page. Lack of knowledge about a policy will not be an
excuse for failing to follow the procedure in it.

Academic Integrity and Plagiarism
UNSW has an ongoing commitment to fostering a culture of learning informed by academic
integrity. All UNSW staff and students have a responsibility to adhere to this principle of academic
integrity. Plagiarism undermines academic integrity and is not tolerated at UNSW. Plagiarism at
UNSW is defined as using the words or ideas of others and passing them off as your own.
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The UNSW Student Code provides a framework for the standard of conduct expected of UNSW
students with respect to their academic integrity and behaviour. It outlines the primary
obligations of students and directs staff and students to the Code and related procedures.

In addition, it is important that students understand that it is not permissible to buy
essay/writing services from third parties as the use of such services constitutes plagiarism
because it involves using the words or ideas of others and passing them off as your own. Nor is
it permissible to sell copies of lecture or tutorial notes as students do not own the rights to this
intellectual property.

If a student breaches the Student Code with respect to academic integrity, the University may take
disciplinary action under the Student Misconduct Procedure.

Plagiarism
Plagiarism is presenting another person's work or ideas as your own. Plagiarism is a serious
breach of ethics at UNSW and is not taken lightly. So how do you avoid it? 

Additional Support

ELISE (Enabling Library and Information Skills for Everyone)
ELISE is designed to introduce new students to studying at UNSW.
Completing the ELISE tutorial and quiz will enable you to:
 analyse topics, plan responses and organise research for academic writing and other
assessment tasks
 effectively and efficiently find appropriate information sources and evaluate relevance
to your needs
 use and manage information effectively to accomplish a specific purpose
 better manage your time
 understand your rights and responsibilities as a student at UNSW
 be aware of plagiarism, copyright, UNSW Student Code of Conduct and Acceptable Use of
UNSW ICT Resources Policy
 be aware of the standards of behaviour expected of everyone in the UNSW community
 locate services and information about UNSW and UNSW Library

Some of these areas will be familiar to you, others will be new. Gaining a solid understanding of all

Equitable Learning Services (ELS)
If you suffer from a chronic or ongoing illness that has, or is likely to, put you at a serious
disadvantage, then you should contact the Equitable Learning Services (previously known as
SEADU) who provide confidential support and advice.

They assist students:

• living with disabilities
• with long- or short-term health concerns and/or mental health issues
• who are primary carers
• from low SES backgrounds
• of diverse genders, sexes and sexualities
• from refugee and refugee-like backgrounds
• from rural and remote backgrounds
• who are the first in their family to undertake a bachelor-level degree.

Equitable Learning Services (ELS) may determine that your condition requires special
arrangements for assessment tasks. Once the School has been notified of these, we will make
every effort to meet the arrangements specified by ELS.

Additionally, if you have suffered significant misadventure that affects your ability to complete the
course, please contact your Lecturer-in-charge in the first instance.

Academic Skills Support and the Learning Centre
The Learning Centre offers academic support programs to all students at UNSW Australia. We
assist students to develop approaches to learning that will enable them to succeed in their
academic study. 
Applications for Special Consideration for Missed Assessment
Please adhere to the Special Consideration Policy and Procedures provided on the web page below
when applying for special consideration.


Please note that the application is not considered by the Course Authority, it is considered by a
centralised team of staff at the Nucleus Student Hub.
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The School will contact you (via student email account) after special consideration has been
granted to reschedule your missed assessment, for a lab test or paper-based test only.

For applications for special consideration for assignment extensions, please note that the new
submission date and/or outcome will be communicated through the special consideration web site
only, no communication will be received from the School.

For Dates on Final Term Exams and Supplementary Exams please check the “Key Dates for
Exams” ahead of time to avoid booking holidays or work obligations.