## Overview

MATH5868 is an Honours and Postgraduate Coursework Mathematics course. See the course overview below.

Units of Credit: 6

Prerequisites: N/A

Exclusion: N/A

Cycle of offering: Term 3

Course Enrolment Constraints: There are no prerequisites for this course. However, students are assumed to be acquainted with the basic principles of Probability and Statistics theory: random variables and their characteristics, estimators and their properties (bias, variance, consistency, asymptotic distribution), law of large numbers and central limit theorem, maximum likelihood methods. Moreover, they are expected to have basic knowledge of Real Analysis: functions and their properties, limits and series, differentials and integrals, Taylor expansions and function spaces.

Important additional information as of 2023

#### UNSW Plagiarism Policy

The University requires all students to be aware of its policy on plagiarism.

For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.

If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH5868 you can log into UNSW Moodle for this course.

## Course aims

The course aims to present and promote the basic techniques of resampling methods useful in statistics. Those methods are popular as they offer reliable alternatives to traditional asymptotic approaches, mostly based on Central Limit Theorems.

The bootstrap is attractive in many applications when determining the sampling distribution of a statistic of interest (estimator or test statistic). In many situations, the quality of the approximation is better than its asymptotic counterpart, while in some others, the asymptotic approximation is not available and the bootstrap turns out to be the only possibility for statistical inference. The resampling methods are first introduced in a general framework and their theoretical properties are investigated. Then, they are illustrated through many standard problems of statistical inference and common questions in related fields.

## Course descriptions

The course presents the basic techniques of resampling methods useful in statistics. These have grown very popular over the last two decades as they offer reliable alternatives to traditional asymptotic approaches, mostly based on Central Limit Theorems. The flagship instance of resampling-based approaches is the so-called `bootstrap', by now considered as a real breakthrough in statistics. A very versatile technique, the bootstrap allows easy determination of the sampling distribution of any statistic of interest (estimator or test statistic) in a variety of situations. In fact, the bootstrap bypasses heavy analytical developments by substituting appropriate simulations. In many cases, the quality of the bootstrap approximation is better than its asymptotic counterparts, while in other situations, there is no asymptotic approximation available and the bootstrap turns out to be the only possibility for statistical inference.

In this course, the bootstrap and other related resampling methods are first introduced in a general framework and their theoretical properties are investigated. Then, they are illustrated through many standard problems of statistical inference and common questions in related fields.