This course follows on from STAT3013 by providing a more advanced treatment of large sample approximation theory and some of its applications to statistical inference.  The focus will be on developing a deeper theoretical understanding of some of the important statistical methods by developing the underlying theory. The objectives will be to achieve a deep understanding of particular statistical methods and to learn to use some advanced tools for analysing and developing statistical methods.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Carry out maximum likelihood estimation and inference in simple statistical models with several parameters.
2. Apply Taylor series expansions to derive approximate sampling distributions and confidence intervals for transformed estimators.
3. Explain the basic concepts of robust estimation in statistics, be able to derive influence functions of estimators and use them to evaluate the robustness of estimators.
4. Explain the different uses of randomisation in statistics.
5. Discuss and use basic principles of statistical inference and the issues they raise about how to do statistical inference.

Research-Led Teaching

This course draws on the active research interests of the course convenor. These include the directly relevant topics of Statistical Inference, Statistical Modelling, Robustness, Nonparametric and Semi-Parametric methods, Analysis of Sample Surveys.

Examination Material or equipment

The final assessment will be a 2 hour in person, closed book examination held during the university examination period at the end of semester.

No electronic aids are permitted (e.g. laptops, phones, calculators)

The use of dictionaries during the exam is not permitted.

Students may bring one handwritten (single side) A4 page of notes to the examination.

Students must return the examination paper and all rough work and notes made during the examination at the end of the examination.

Required Resources

Class materials, including lecture recordings, slides, weekly assignments, weekly tutorials and other relevant materials, will be made available on the class web page on Canvas. It is essential that you visit the class Canvas site regularly. Important: you will need to be correctly enrolled in the course before you can access the Canvas site.

The application of modern statistical techniques requires familiarity with some statistical computing package and some assignments for this course will require some analysis on a computer. This course makes use of the R computing package, which is freely available to download at http://www.r-project.org. Further instructions on R, including a series of revision workshops, will be made available on the Canvas site for this course. R is also available on all InfoCommons computers on the ANU campus.

Recommended Resources

The main reference will be

Welsh, A.H. (1996). Aspects of Statistical Inference. New York: Wiley.

The ANU Library has the e-book .

Other books on statistical inference in general and on specific topics such as robustness, sample surveys etc may be useful to students.

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• verbal comments
• feedback to whole class, groups, individuals, focus group etc

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Other Information

Announcements

Students are expected to check the Canvas site for updates, changes and announcements about this course.

Communication via email

If I or anyone in the School, College or ANU administration need to contact you, we will do so via your official ANU student email address, which you need to check regularly. If you need to email me or the tutor, you must do so using your ANU email address. Emails from personal email accounts will not be answered.

Computing

The application of modern statistical techniques requires familiarity with one or more statistical computing packages. In this course we will use the R statistical computing package to do some numerical calculations, to develop examples and to illustrate points made in the lectures. R can be downloaded for free from the internet.

Assessment requirements

Students are required to complete the weekly exercises or quizzes themselves, without the using artificial intelligence or ghostwriting services.

Referencing

In all assessments (including exams and exercises or quizzes), students must reference any results, words or ideas taken from any other source. A guide can be found at https://academicskills.anu.edu.au/resources/handouts/referencing-basics .

Scaling

Your final marks will be based on the raw marks awarded for each of the assessment items. However, your final mark may not be the same as the number produced by that formula, as the marks may be scaled. Any scaling applied will preserve the rank order of the raw marks, but may be either up or down.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Review of likelihood theory	Workshops and tutorials commence
2	Large sample theory
3	Likelihood-based confidence intervals and tests
4	Introduction to robustness
5	Functional calculus and influence functions
6	More on robustness
7	Randomisation
8	Randomisation as a basis for inference
9	More on randomisation and inference
10	The likelihood principle
11	Sufficiency and the sufficiency principle
12	Ancillarity and the the conditionality principle	Workshops and tutorials end

Tutorial Registration

Tutorials will be held weekly on campus, starting in Week 1 and running through Week 12. Students should enrol in their tutorial using MyTimetable.

"ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage (https://www.anu.edu.au/students/program-administration/timetabling)".

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Participation in weekly discussions	10 %	27/07/2026	30/10/2026	1,2,3,4,5
Weekly exercises (weeks 1-5, 7-11)	20 %	27/07/2026	30/10/2026	1,2,3,4,5
In-class assessment (week 6)	5 %	04/09/2026	24/09/2026	1,2,3,4,5
In-class assessment (week 12)	5 %	30/10/2026	09/12/2026	1,2,3,4,5
Final exam	60 %	05/11/2026	09/12/2026	1,2,3,4,5

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines , which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Skills website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Canvas’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

Course content delivery will take the form of pre-recorded weekly lectures (available on Canvas), weekly in-person 1-hour lecture discussion sessions (recorded), weekly in-person 2-hour workshops (recorded) and weekly tutorials, all delivered on campus.

Examination(s)

Centrally administered examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information.

The final assessment will be a 2 hour in person, closed-book examination held during the university examination period at the end of semester. The examination (which is worth 50% of the assessment) will cover the entire course content and is to be completed individually. 

No electronic aids are permitted (e.g. laptops, phones, calculators)

The use of dictionaries during the exam is not permitted.

Students may bring one handwritten (single side) A4 page of notes to the examination.

Students must return the examination paper and all rough work and notes made during the examination at the end of the examination.

Students will be provided with further details regarding the exam by the end of week 10.

Assessment Task 1

Participation in weekly discussions

This is a continuous assessment component throughout the semester. Students are expected to attend and contribute to the weekly Workshop session by asking questions and participating in the discussion. In this task, you will be assessed on your demonstration of the required learning outcomes of the course as exhibited through the questions asked and responses given in tutorials. Students will be given regular informal feedback on their performance in this assessment whilst formal marking of this component will be provided to students by the end of Week 6 and 12.

Assessment Task 2

Weekly exercises (weeks 1-5, 7-11)

A take-home task will be set in each week 1-5 and 7-11. Take-home tasks must be submitted through Turnitin at least 15 minutes before the start of the following Workshop session. As these problems will be discussed in the workshop session, no late submissions will be accepted. The weekly tasks will be equally weighted. Students who are unable to submit one or more tasks and produce valid medical certificate(s) will have their completed tasks reweighted to adjust for the missing task(s). The submitted solutions will be graded and returned in the following week. The submission is required to be clearly written, free from grammatical or punctuation errors. It should show appropriate mathematical working. Submissions can be neatly handwritten or they can be prepared using mathematical typesetting software such as LATEX. Students are encouraged to check that the marks available via the Canvas gradebook are consistent with the marks written on returned submissions.

Assessment Task 3

In-class assessment (week 6)

In-class assessment will be completed in the 2 hour workshop period. The activities will be similar to the weekly take-home tasks but will be completed individually in class, without the use of electronic devices. Submissions must be neatly handwritten. No late submissions will be accepted. The submitted solutions will be graded and returned after the midsemester break. The submission is required to be clearly written, free from grammatical or punctuation errors. It should show appropriate mathematical working. Students are encouraged to check that the marks available via the Canvas gradebook are consistent with the marks written on returned submissions.

Assessment Task 4

In-class assessment (week 12)

In-class assessment will be completed in the 2 hour workshop period. The activities will be similar to the weekly take-home tasks but will be completed individually in class, without the use of electronic devices. Submissions must be neatly handwritten. No late submissions will be accepted. The submitted solutions will be graded and returned before the end of the exam period. The submission is required to be clearly written, free from grammatical or punctuation errors. It should show appropriate mathematical working. Students are encouraged to check that the marks available via the Canvas gradebook are consistent with the marks written on returned submissions.

Assessment Task 5

Final exam

The final assessment will be a 2 hour in person, closed-book examination held during the university examination period at the end of semester. The examination (which is worth 60% of the assessment) will cover the entire course content and is to be completed individually. 

No electronic aids are permitted (e.g. laptops, phones, calculators)

The use of dictionaries during the exam is not permitted.

Students may bring one handwritten (single side) A4 page of notes to the examination.

Students must return the examination paper and all rough work and notes made during the examination at the end of the examination.

Students will be provided with further details regarding the exam by the end of week 10.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

Take-home assignments are to be submitted online on Canvas via Turnitin. You must attach an assignment cover sheet. Please keep a copy of tasks completed for your records.

Any student identified, either during the semester or in retrospect, as having used ghost writing services will be investigated under ANU's Academic Misconduct Rule. The use of large language models (LLM) or other forms of artificial intelligence (AI) in the preparation of your assessment material is not allowed. You will be required to sign electronically a declaration as part of the submission of your assignment that, except where otherwise formally indicated, the exercise is entirely your own work.

Hardcopy Submission

In-class assignments must be handwritten on paper.

Late Submission

Late submission not permitted. Submission of weekly exercises or quizzes without an extension after the due date will result in the award of a mark of 0.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material. Any use of artificial intelligence must be properly referenced. Failure to properly cite use of Generative AI will be considered a breach of academic integrity.

Returning Assignments

Weekly assessments will be returned in the following teaching week. Marks will be uploaded to the Canvas gradebook for the course. It is the responsibility of students to check that these recorded marks are in agreement with the marks written on returned quizzes.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

No weekly exercises or in-class assignments may be resubmitted.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Accessibility for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents all ANU students