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  • Point Estimation

    This online, interactive lesson on point estimation provides examples, exercises, and applets concerning estimators, method of moments, maximum likelihood, Bayes estimators, best unbiased estimators, and sufficient, complete and ancillary statistics.

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  • Markov Chains

    This online, interactive lesson on Markov chains provides examples, exercises, and applets that cover recurrence, transience, periodicity, time reversal, as well as invariant and limiting distributions.

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  • Resampling Statistics: Randomization and the Bootstrap

    This set of pages describes software the author wrote to implement bootstrap and resampling procedures. It also contains an introduction to resampling and the bootstrap; and examples applying these procedures to the mean, the median, correlation between two groups, and analysis of variance.

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  • BGIM : Maximum Likelihood Estimation Primer

    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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  • Sufficient Statistics

    This page introduces the definition of sufficient statistics and gives two examples of the use of factorization to prove sufficiency.

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  • The Cramer-Rao Lower Bound

    This page introduces the Cramer-Rao lower bound, discusses it's usefulness, and proves the inequality.

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  • Cramer-Rao Lower Bound: an Example

    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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  • Statistical Inference

    This page contains course notes and homework assignments with solutions for a mathematical statistics class. The course covers statistical inference, probability, and estimation principles.

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  • Properties of an Estimator

    These slides address point estimation including unbiasedness and efficiency and the Cramer-Rao lower bound.

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  • Theoretical Underpinnings of the Bootstrap

    This page discusses the theory behind the bootstrap. It discusses the empirical distribution function as an approximation of the distribution function. It also introduces the parametric bootstrap.

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