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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 densitiesperform goodness of fit tests to select a parametric distribution modelfind point and interval estimates for parameters and functions of parameters using maximum likelihood estimationperform hypothesis testing and interpret test results correctly, including likelihood ratio tests and multiple testing
1) MATH103 or MATH199 or EMTH119; or 2) (STAT101 or STAT111 or STAT112) and (MATH102 or EMTH118 or MATH108 or MATH109).
STAT214
Dominic Lee
Attendance and class participation 10%Continual assessment 30% Four Tests (15% each) 60%There will be three lectures and one computer lab per week for this course. Attendance at lectures and computer labs is mandatory because supervised instruction is essential for understanding the course material.The continual assessment consists of a series of exercises that must be submitted at specified times throughout the course. These exercises and their timings are designed to help you keep up with the course material. They also allow the lecturer to monitor progress and to provide assistance in a timely manner when needed.There will be four tests, one every three weeks, but no final exam.
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).
STAT213 Homepage
Domestic fee $647.00
International fee $3,325.00
* 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 .