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This free OpenLearn course, Point estimation, is an extract from the Open University course M347 Mathematical statistics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] , a third level course that provides the mathematical theory underlying the methods and concepts used in practical statistical analyses. Students are expected to have a basic knowledge of the ideas and concepts of statistical science. A considerable amount of mathematics is also sometimes required for the development of theory presented in the course.
Point estimation consists of material from M347 Unit 5, Point estimation, and has two sections in total. You should set aside approximately five hours to study each of the sections; the whole extract should take about 10 hours to study. The extract is a small part (around 4%) of a large course that is studied over eight months, and so can give only an approximate indication of the level and content of the full course.
The topic of this extract is point estimation, that is, the estimation of the value of the parameter of a statistical model by a single number, a point estimate for the parameter. It is relatively self-contained and should be reasonably easy to understand for someone with a good knowledge of statistics, such as could be gained from studying the Open University course M248 Analysing data. The mathematical knowledge required could be gained from studying up to the level of the Open University course MST125 Essential mathematics 2 (or its predecessor MS221 Exploring mathematics). A few techniques and definitions are present in the extract without explanation.
Mathematical/statistical content at the Open University is usually provided to students in printed books, with PDFs of the same online. This format ensures that mathematical notation is presented accurately and clearly. The PDF of this extract thus shows the content exactly as it would be seen by an Open University student. However, the extract isn't entirely representative of the module materials, because there are no explicit references to use of the M347 software or to video material (although please note that the PDF may contain references to other parts of M347). In this extract, some illustrations have also been removed due to copyright restrictions.
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Section 1 develops some aspects of maximum likelihood estimation. In particular, you will find out how to obtain the maximum likelihood estimator of an unknown parameter, using calculus. You will need to do lots of differentiation in this section.
Section 2 introduces a number of important properties of point estimation.