Statistics Final Year Topic: Classification Error of Linear and Quadratic Discriminant Rules under Unequal Covariances

This Statistics final year project uses simulated labelled multivariate training and independent test sets to investigate a specific question in multivariate inference. The analysis is designed around known generating conditions so that the behaviour of competing statistical procedures can be checked.

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Why choose this project topic?

This study makes discriminant assumptions an explicit, reproducible comparison. Working with simulated labelled multivariate training and independent test sets lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How do covariance inequality and training-sample size affect linear and quadratic discriminant classification error?

Agree the scenario ranges, sample sizes and reporting measures for discriminant assumptions before running the study.

Proposed project objectives

01Specify the data-generating conditions for simulated labelled multivariate training and independent test sets.
02Implement a reproducible analysis of discriminant assumptions with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How do covariance inequality and training-sample size affect linear and quadratic discriminant classification error?

A suggested research approach

Vary covariance structure while holding class proportions and mean separation explicit. Compare held-out error, covariance-estimation instability and the effect of regularisation where declared in advance. Write the analysis before inspecting favourable runs, record random seeds where simulation is used, and keep generated study data distinct from observed field data.

What you will need

A written design for simulated labelled multivariate training and independent test sets
Statistical software supporting multivariate inference and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

A more flexible covariance model can perform worse with limited data, and simulation accuracy does not establish deployment fitness.

Statistics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

Chapter 1Introduction
Chapter 2Literature Review
Chapter 3Theory and Methodology
Chapter 4Results and Applications
Chapter 5Summary, Conclusion and Recommendations

Turn this topic into your own final year project.

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