STAT213-15S2 (C) Semester Two 2015

Statistical Inference

15 points

Details:
Start Date: Monday, 13 July 2015
End Date: Sunday, 15 November 2015
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 26 July 2015
  • Without academic penalty (including no fee refund): Sunday, 11 October 2015

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

Prerequisites

(STAT101 or STAT111 or STAT112) and (MATH102 or EMTH118 or MATH108 or MATH109); or any one of MATH103, MATH199, EMTH119.

Restrictions

STAT214

Course Coordinator / Lecturer

Marco Reale

Assessment

Assessment Due Date Percentage 
Assignments (x4) 40%
Final Examination 60%

Textbooks / Resources

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 $699.00

International fee $3,450.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All STAT213 Occurrences

  • STAT213-15S2 (C) Semester Two 2015
Previous year Next year