STAT41080 Mathematical Statistics

Academic Year 2023/2024

An overview of mathematical statistics will be presented and placed in the context of modern statistical problems. Both single and multiparameter methods will be examined. The introduction will cover maximum likelihood, likelihood ratio and Fisher information. Then large sample results will be derived heuristically - distribution of the MLE, the score statistic and likelihood ratio statistic. Bias and variability of point estimates will be examined including the method of moments, bootstrap method, MLE together with a proof of the Cramer-Rao lower bound. Confidence intervals and coverage probability will be discussed. Bayesian estimators will also be discussed.

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Curricular information is subject to change

Learning Outcomes:

On successful completion of this module students should be able to demonstrate knowledge of the basic parametric models used in statistics. In particular, the topics of point estimation, interval estimation and testing. They should be able to derive large sample results and identify when they are appropriate. They should be able to explain the delta method, jackknife, the bootstrap and results relating to variability.They should be able to use the basic tools of classical statistics and demonstrate knowledge of how to use them in modern statistical problems. They should have a basic understanding of Bayesian models and their role in modern statistics.

Indicative Module Content:

Maximum likelihood; Invariance; Score statistic; Fisher information; Cramer-Rao lower bound; Large sample results: Central limit theorem, consistency and asymptotic normality of the mle; Likelihood ratio statistics and asymptotic distribution; delta method, jackknife, bootstrap, method of moments, Bayesian estimation; confidence intervals and coverage probability.

Student Effort Hours: 
Student Effort Type Hours
Lectures

24
Tutorial

11
Autonomous Student Learning

65
Total

100
Approaches to Teaching and Learning:
The module will consist of lecturers with typed notes and worked examples in class. 
Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Not applicable to this module.
 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Problem sets Throughout the Trimester n/a Standard conversion grade scale 40% No

30
Examination: End of semester examination 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

70

Carry forward of passed components
No
 
Resit In Terminal Exam
Summer Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Thais Pacheco Menezes Tutor
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
 
Spring
      
Tutorial Offering 1 Week(s) - 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Fri 14:00 - 14:50
Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Wed 11:00 - 11:50
Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Wed 13:00 - 13:50
Spring