Next week I will teach my students the score function and its variance (i.e.: fisher information).

I am looking for way(s) to illustrate these concepts so to help my students understand them (and not just calculate them for various distributions, which is what is often done in class).

Any suggestions would be helpful (beyond giving me links to What is the intuition behind the score function? and Likelihood score function 101)


Buse, A (1982). The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician, 36:3a, 153-157 is an excellent reference with one major reservation: Lagrange multiplier test should have been called Rao's efficient score test. I wrote Prof. Rao about this when the paper came out to let him know my frustration that incorrect terminology was being used and he was thankful. Other than that it's an excellent article. I've sent you a personal email with the pdf.

Another article by Linda Pickle is also excellent - Stat Comp & Stat Graphics Newsletter Nov. 1991 which I'm sending to you.

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    $\begingroup$ Thank you Frank. I'll say the first reference is interesting. It relies on too many notions for the early stage of the course (not all students know what hypothesis testing or CI are). But I may use it later on. What I ended up doing was to make several plots of the log likelihood of the normal distribution (for estimating mu), with the tangent line, and for samples of n=5 and n=100 - thus demonstrating the variance of the score function (and how it relates to a more curvy likelihood). $\endgroup$ – Tal Galili Mar 17 '16 at 22:30

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