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Overview

Course Prescription

Fundamental topics in estimation and statistical inference. Advanced topics in modelling including regression with dependent data, survival analysis, methods to handle missing data. Advanced topics in current statistical practice researched by students. Students will undertake and present individual research projects on assigned topics, consisting in a literature search and a computational application to a data analysis task.

Course Overview

STATS 730 consists of interactive lectures covering classical and advanced aspects of statistical inference and individually assigned research projects to be presented in class. The lecture component consists in an introduction to simple maximum likelihood concepts is followed by a discussion of point estimators, including methods to find them and key properties such as mean squared error, sufficiency, ancillarity, and unbiasedness. (Asymptotic efficiency is also discussed in the second half of the course.) The Halmos-Savage, Rao-Blackwell and Cramér-Rao theorem are discussed and applied. This segment is followed by an in-depth consideration of the likelihood-based frequentist approach to inference. Simple and not-so-simple (e.g., finite mixture model) examples based on independent and identically distributed samples are presented. The essential properties, concepts and tools of maximum-likelihood inference are then presented, with an equal focus on theory, such as asymptotic evaluations, and on applications. Maximum likelihood and extensions are applied in a wide variety of settings with examples in R, with special attention to exponential families applied to generalised linear modelling. The course concludes by looking at extensions of maximum likelihood for models for more challenging situations, including quasi-likelihood and conditional likelihood. 

The research component consists in an assigned project to be completed in two phases, based on an assigned topic, a research question and a given data set: 1) a literature review and description of the methods to be applied to answer the research question  using the data; 2) the results of the analysis. Each phase will be presented by the students, and be the object of an assessed in-class quiz co-created by the presenting students and the instructors. The topics involved will be varied and current, some of them taken from methods for dependent data, survival analysis, methods to handle missing data, predictive analytics, causal inference, semi-parametric inference, and others.

Prior familiarity with R is strongly advised for those undertaking this course.

Key Topics

  • Introduction to likelihood and principles of inference
  • Parametric families of distributions, including natural exponential families and exponential dispersion models
  • Methods of finding point estimators
  • Properties of point estimators
  • Essential concepts and iid examples
  • Large-sample methods, including hypothesis tests and profile likelihood-based confidence intervals/regions
  • Delta-method, critical look at Wald-based inference
  • Maximising the likelihood in practice
  • Asymptotic evaluations
  • Generalised linear models and extensions
  • Quasi-likelihood, Generalised estimating equations and Linear mixed models

Workload Expectations

This course is a Level 9 15-point course and students are expected to spend 150 hours per semester involved in each 15-point course that they are enrolled in.

The breakdown is as follows:

- Outside the mid-semester break, a typical weekly workload includes:

  • 4 hours of lectures
  • 2 hours reviewing the course content
  • 5 hours of work on project and/or test preparation
- During the mid-semester break, students are expected to spend 18 hours of work on their project.

Course Prerequisites, Corequisites and Restrictions

Prerequisite

Locations and Semesters Offered

LocationSemester
City

Teaching and Learning

Campus Experience

Attendance is expected at scheduled activities  to complete components of the course.
Lectures will be available as recordings. 
The course will not include live online events.
Attendance on campus is required for the term tests.
The activities for the course are scheduled as a standard weekly timetable.

Learning Resources

Taught courses use a learning and collaboration tool called Canvas to provide students with learning materials including reading lists and lecture recordings (where available). Please remember that the recording of any class on a personal device requires the permission of the instructor.

Additional Information on Learning Resources

Lecture Slides:

  • Lecture slides will be available on Canvas. The lecture slides, along with the assignment material, will contain all the information needed to undertake the course successfully
Recommended Reading:
  • Maximum Likelihood Estimation and Inference, with Examples in R, SAS and ADMB, by Millar RB. (2011). John Wiley & Sons. (The textbook will be available at no cost in PDF format on Canvas)
  • Statistical Inference, by Casella G & Berger R. (2002). 2nd ed. Duxbury.

Copyright

The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.


You may copy the course content for the purposes of private study or research, but you may not upload onto any third-party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

Other Information

The elevation of STATS 730 to level 9 will be trialled for the first time in 2025. Although no assignments are planned as formative assessments, exercises will be handed out and expected to be worked out by the students in preparation for the two class tests.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

Similarly, research students must meet the University’s expectations of good research practice. This requires:

  • Honesty - in all aspects of research work
  • Accountability - in the conduct of research
  • Professional courtesy and fairness – in working with others
  • Good stewardship – on behalf of others
  • Transparency – of research process and presentation of results
  • Clarity - communication to be understandable, explainable and accessible

For more information on the University’s expectations of academic integrity, please see the Academic Conduct section of the University policy hub.

Disclaimer

Elements of this outline may be subject to change. The latest information about taught courses is made available to enrolled students in Canvas.

Students may be asked to submit assessments digitally. The University reserves the right to conduct scheduled tests and examinations online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.


Assessment and Learning Outcomes

Special Requirements

The practical work will consist in a report in two parts (literature review and methods, results and discussion) that will each be presented  in class and assessed at the end of the first and second half of the semester.

The tests will be held during class time.

The student-project-related quizzes will be held at the end of each presentation.

Course Learning Outcomes

CLO #OutcomeProgramme Capability Link
1
2
3
4
5
6
7
8

Assessments

Assessment TypeAssessment PercentageAssessment Classification

Assessment to CLO Mapping

Assessment Type12345678

Student Feedback, Support and Charter

Student Feedback

Feedback on taught courses is gathered from students at the end of each semester through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback and respond with summaries and actions. Your feedback helps teachers to improve the course and its delivery for future students. In addition, class Representatives in each class can take feedback to the department and faculty staff-student consultative committees.

Additional Information on Student Feedback

New course for 2025: student feedback will be taken into account when reviewing the course. 

Based on recent student feedback, supplementary examples will be introduced when discussing properties of point estimators, which is a more theoretical topic.

Class representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.

Tuākana

Tuākana is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at Tuakana Learning Communities.

Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website.

Wellbeing

We all go through tough times during the semester, or see our friends struggling. There is lots of help out there - please see the Support Services page for information on support services in the University and the wider community.

Special Circumstances

If your ability to complete assessed work is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due. If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page. This should be done as soon as possible and no later than seven days after the affected test or exam date.

Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter.

Student Academic Complaints and Disputes

Students with concerns about teaching including how a course is delivered, the resources provided, or supervision arrangements, have the right to express their concerns and seek resolution. The university encourages informal resolution where possible, as this is quicker and less stressful. For information on the informal and formal complaints processes, please refer to the Student Academic Complaints Statute in the Student Policies and Guidelines section of the Policy Hub.