Conclusion

Following completion of this free OpenLearn course, Point estimation, you should have a clearer understanding of the mathematical basis of classical methods of point estimation.

You should now be able to:

• calculate the maximum likelihood estimator using calculus
• work with the log-likelihood instead of the likelihood itself
• understand that maximum likelihood estimation of a function of a parameter is equivalent to taking that function of the maximum likelihood estimator
• define and calculate the bias of an estimator and choose between unbiased estimators on the basis of their variances
• understand and calculate the Cramèr-Rao lower bound for the variance of any unbiased estimator.

This free OpenLearn course 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)] .

If you feel you are ready to move on in your study of statistics but don’t have time to study a full Open University course at this time, you might like to study the free OpenLearn courses Univariate continuous distribution theory, another adapted extract from the Open University course M347 Mathematical statistics, or Modelling events in time, an adapted extract from the Open University course M343 Applications of probability.

If you are interested in pure mathematics, you might like to try the free OpenLearn courses Number theory, Group theory, Rings and polynomials and Metric spaces and continuity.

If you are interested in applied mathematics, you might like to try the free OpenLearn courses Linear programming – the basic ideas, Introduction to the calculus of variations and Kinematics of fluids.