Posts Tagged ‘ mathematics ’

Mathematical Statistics Lesson of the Day – Basu’s Theorem

Mathematical Statistics Lesson of the Day – Basu’s Theorem

Today’s Statistics Lesson of the Day will discuss Basu’s theorem, which connects the previously discussed concepts of minimally sufficient statistics, complete statistics and ancillary statistics.  As before, I will begin with the following set-up. Suppose that you collected data in order to estimate a parameter .  Let be the probability density function (PDF) or probability […]

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A dynamic programming solution to A/B test design

July 6, 2015
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A dynamic programming solution to A/B test design

Our last article on A/B testing described the scope of the realistic circumstances of A/B testing in practice and gave links to different standard solutions. In this article we will be take an idealized specific situation allowing us to show a particularly beautiful solution to one very special type of A/B test. For this article … Continue reading A dynamic programming solution to A/B test design →

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Mathematical Statistics Lesson of the Day – An Example of An Ancillary Statistic

Mathematical Statistics Lesson of the Day – An Example of An Ancillary Statistic

Consider 2 random variables, and , from the normal distribution , where is unknown.  Then the statistic has the distribution . The distribution of does not depend on , so is an ancillary statistic for . Note that, if is unknown, then is not ancillary for .Filed under: Mathematical Statistics, Statistics, Statistics Lesson of the […]

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Mathematics and Applied Statistics Lesson of the Day – Contrasts

Mathematics and Applied Statistics Lesson of the Day – Contrasts

A contrast is a linear combination of a set of variables such that the sum of the coefficients is equal to zero.  Notationally, consider a set of variables . Then the linear combination is a contrast if . There is a reason for why I chose to use as the symbol for the variables in […]

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My Favourite Book

April 15, 2015
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My Favourite Book

Well, perhaps it's not really my favourite book, but it's certainly right up there with the most heavily thumbed tomes on my office bookshelf.I'm referring to Tables of Integrals, Series and Products, by Gradshteyn and Ryzhik. I picked up a used copy o...

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Optimal Design of Experiments

January 11, 2015
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Optimal Design of Experiments

The first colloquium speaker at this semester, professor Wei Zheng from IUPUI, will give a talk on “Universally optimal designs for two interference models“. In this data explosive age, people are easy to get big data set, which renders people difficult to make inferences from such massive data. Since people usually think that with more […]

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Econometricians’ Debt to Alan Turing

December 31, 2014
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Econometricians’ Debt to Alan Turing

The other day, Carol and I went with friends to see the movie, The Imitation Game. I definitely recommend it.I was previously aware of many of Alan Turing's contributions, especially in relation to the Turing Machine, cryptography, computing, and artif...

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Machine Learning Books Suggested by Michael I. Jordan from Berkeley

December 30, 2014
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Machine Learning Books Suggested by Michael I. Jordan from Berkeley

There has been a Machine Learning (ML) reading list of books in hacker news for a while, where Professor Michael I. Jordan recommend some books to start on ML for people who are going to devote many decades of their lives to the field, and who want to get to the research frontier fairly quickly. […]

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Mathematical Statistics Lesson of the Day – Complete Statistics

Mathematical Statistics Lesson of the Day – Complete Statistics

Filed under: Mathematical Statistics, Mathematics, Probability, Statistics, Statistics Lesson of the Day Tagged: almost surely, complete statistic, completeness, estimation, mathematical statistics, point estimation, probability, probability density function, probability mass function, statistics, unbiased estimation, unbiased estimator

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Christian Robert Shows that the Sample Median Cannot Be a Sufficient Statistic

Christian Robert Shows that the Sample Median Cannot Be a Sufficient Statistic

I am grateful to Christian Robert (Xi’an) for commenting on my recent Mathematical Statistics Lessons of the Day on sufficient statistics and minimally sufficient statistics. In one of my earlier posts, he wisely commented that the sample median cannot be a sufficient statistic.  He has supplemented this by writing on his own blog to show that […]

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