# THEORY OF STATISTICS

STA4TS

2017

Credit points: 15

## Subject outline

This subject builds on the knowledge of classical statistical inference developed in either STA3SI (Statistical Inference) or STA4SI (Statistical Inference). It consists of a selection of material from the following chapters of Casella and Berger (2002): Chapter 6 (Principles of Data Reduction), Chapter 7 (Point Estimation), Chapter 8 (Hypothesis Testing), Chapter 9 (Interval Estimation) and Chapter 10 (Asymptotic Evaluations). This also includes an introduction to the effect of model selection on confidence intervals.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorPaul Kabaila

Subject year levelYear Level 4 - UG/Hons/1st Yr PG

Exchange StudentsYes

## Subject particulars

### Subject rules

Prerequisites STA3SI or STA4SI or enrolment into SMDS.

Co-requisitesN/A

Incompatible subjects STA5TS

Equivalent subjectsN/A

Special conditions A sufficient background in probability and statistics is required to undertake this subject.

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsStatistical Inference, 2nd edition (2002)RecommendedRecommended text: Casella, G. and Berger, R.L..

## Graduate capabilities & intended learning outcomes

01. Present clear proofs of fundamental results in the advanced theory of statistical inference given in the lectures.

Activities:
Active participation in lectures. Preparation for the exam, which consists solely of proofs and sections of proofs from the lecture slides.
Literacies and Communication Skills (Writing)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

02. Derive mathematical calculations to investigate properties of data reduction by sufficiency, data reduction by ancillarity, data reduction by invariance, the assessment of confidence intervals and the effect of model selection on confidence intervals.

Activities:
Active participation in lectures. Also, solving assignment questions relating to these topics.
Literacies and Communication Skills (Writing)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Personal and Professional Skills (Autonomy and independence)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

03. Write clear, well structured and rigorous proofs of results in the theory of statistical inference that the students have not seen in lectures. This includes appropriate use of statistical and mathematical vocabulary and notation.

Activities:
Assignments given out every week or second week involve theoretical derivations of results not stated in lectures. Each assignment consists of up to 100% assessed theoretical derivations.
Literacies and Communication Skills (Writing)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Personal and Professional Skills (Autonomy and independence)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

04. Describe some important implications for statistical practice of the advanced theory of statistical inference.

Activities:
Active participation in lectures. Also, solving assignment questions relating to these implications.
Literacies and Communication Skills (Writing)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Inquiry and Analytical Skills (Critical Thinking,Creative Problem-solving,Inquiry/Research)
Personal and Professional Skills (Autonomy and independence)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

## Subject options

Select to view your study options…

Start date between: and    Key dates

## Melbourne, 2017, Semester 1, Day

### Overview

Online enrolmentNo

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorPaul Kabaila

### Class requirements

Lecture Week: 10 - 22
Two 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

### Assessments

Final examination (2-hour short answer)60 01, 02, 04
Seven assignments (approx. 400 words each)40 01, 02, 03, 04

## Melbourne, 2017, Semester 2, Day

### Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorPaul Kabaila

### Class requirements

Lecture Week: 31 - 43
Two 1.0 hours lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.