STAT213-18S2 (C) Semester Two 2018

# Statistical Inference

 15 points16 Jul 2018 - 18 Nov 2018

## Description

This course provides the theoretical foundations for statistical estimation and testing at an introductory level. These are essential for more advanced studies in statistics at higher levels because they facilitate a deeper understanding of statistical techniques and their applications.

To illuminate key ideas in estimation and testing, the course will focus mainly on inference for independent and identically distributed univariate data.

Topics that are usually covered include:

• fundamentals of probabilistic modelling: Probabilities, distribution functions, densities, expectations, quantiles
• estimating expectations and probabilities: Law of large numbers, central limit theorem, confidence bounds and intervals
• estimating distribution functions: Empirical distribution function, Glivenko-Cantelli theorem, Dvoretzky-Kiefer-Wolfowitz inequality
• estimating quantiles: Exact and approximate methods
• estimating densities: Histograms
• fundamentals of parametric modelling: Common parametric distributions moment generating function, method of moments, goodness of fit tests, generating random variables with prescribed distributions, rudiments of Monte Carlo simulation, parametric bootstrap
• maximum likelihood estimation, Likelihood function, invariance, consistency, asymptotic normality and efficiency.
• fundamentals of hypothesis testing: Null and alternative hypotheses, type 1 and 2 errors, test statistic, significance level, rejection region, power function, p-value
• likelihood ratio tests
• multiple testing

Statistical computations will be performed using the R software but students do not need to know R beforehand.

## Learning Outcomes

Through this course, you will be able to:

• find point and interval estimates for expectations, probabilities, distribution functions, quantiles and densities
• perform goodness of fit tests to select a parametric distribution model
• find point and interval estimates for parameters and functions of parameters using maximum likelihood estimation
• perform hypothesis testing and interpret test results correctly, including likelihood ratio tests and multiple testing

This course will provide students with an opportunity to develop the Graduate Attributes specified below:

 Critically competent in a core academic discipline of their award Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

## Pre-requisites

STAT101 and (MATH102 or EMTH118); or any one of MATH103, MATH199, EMTH119.

STAT214

## Timetable 2018

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Thursday 11:00 - 12:00 A8 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct Lecture B 01 Wednesday 16:00 - 17:00 Ernest Rutherford 140 16 Jul - 26 Aug 10 Sep - 21 Oct Lecture C 01 Tuesday 15:00 - 16:00 A8 Lecture Theatre 16 Jul - 26 Aug 10 Sep - 21 Oct Tutorial A 01 Monday 12:00 - 13:00 Jack Erskine 241 23 Jul - 26 Aug 10 Sep - 21 Oct 02 Friday 09:00 - 10:00 Jack Erskine 242 23 Jul - 26 Aug 10 Sep - 21 Oct 03 Tuesday 16:00 - 17:00 West 213A 23 Jul - 26 Aug 10 Sep - 21 Oct

## Textbooks

Course materials will be provided and no textbook is needed. After enrolling in the course, you will be able to access materials from the course web page in Learn at: http://www.learn.canterbury.ac.nz/

Students who have not used the R software before can refer to the following e-book available from the UC Library:

A Beginner’s Guide to R, by Zuur, Ieno and Meesters (Springer, 2009).

## Indicative Fees

Domestic fee \$749.00

International fee \$3,788.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

## All STAT213 Occurrences

• STAT213-18S2 (C) Semester Two 2018