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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 testingStatistical computations will be performed using the R software but students do not need to know R beforehand.
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.
STAT101 and (MATH102 or EMTH118); or any one of MATH103, MATH199, EMTH119.
Students must attend one activity from each section.
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).
General information for students
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.