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Estimation Principles

  • This set of pages is an introduction to Maximum Likelihood Estimation. It discusses the likelihood and log-likelihood functions and the process of optimizing.
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  • This page introduces the definition of sufficient statistics and gives two examples of the use of factorization to prove sufficiency.
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  • This page introduces the Cramer-Rao lower bound, discusses it's usefulness, and proves the inequality.
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  • This file applies the Cramer-Rao inequality to a binomial random variable to prove that the usual estimator of p is a minimum variance unbiased estimator.
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  • These slides address point estimation including unbiasedness and efficiency and the Cramer-Rao lower bound.
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  • A useful site for instructors to learn how to create and incorporate guided notes into their classroom.
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  • This site gives an explanation of, a definition for and an example of confidence intervals. It covers topics including inference about population mean and z and t critical values.
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  • This online, interactive lesson on distributions provides examples, exercises, and applets which explore the basic types of probability distributions and the ways distributions can be defined using density functions, distribution functions, and quantile functions.
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  • This Java based applet gives students an opportunity to work through confidence interval problems for the mean. The material provides written word problems in which an individual must be able to correctly identify the given parts for a confidence interval calculation, and then be able to use this information to find the confidence interval. It gives step by step prompts to encourage students to choose the correct numbers and "cast of characters".
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  • This site provides a collection of applets and their descriptions. Some of the titles include the Monte Carlo Estimation of Pi, Can You Beat Randomness?, One-Dimensional Random Walk, Two-Dimensional Random Walk, The Anthill and Molecular Motion, Diffusion Limited Aggregation, The Self-Avoiding Walk, Fractal Coastlines, and Forest Fires and Percolation.
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