Recursions for the Moments of Some Discrete Distributions

You could say, "Moments maketh the distribution". While that's not quite true, it's pretty darn close.

The moments of a probability distribution provide key information about the underlying random variable's behaviour, and we use these moments for a multitude of purposes. Before proceeding, let's be sure that we're on the same page here.

2019 Econometric Game Results

The Econometric Game is over for another year.

The winning team for 2019 was from the University of Melbourne.

The second and third placed teams were from the Maastricht University and Aarhus University, respectively.

Congratulations to the winning teams, and to all who competed this year!

© 2019, David E. Giles

EViews 11 Now Available

As you'll know already, I'm a big fan of the EViews econometrics package. I always found it to be a terrific, user-friendly, resource when teaching economic statistics and econometrics, and I use it extensively in my own research.

Along with a lot of other EViews users, I recently had the opportunity to "test drive" the beta release of the latest version of this package, EViews 11. 

EViews 11 has now been officially released, and it has some great new features. (Click on the links there to see some really helpful videos.) To see what's now available, check it out here. 

Nice update. Thanks!

© 2019, David E. Giles

SHAZAM!

This past weekend the new movie, Shazam, topped the box-office revenue list with over US$53million - and this is it's first weekend since being released.

Not bad!

Of course, in the Econometrics World, we associate the word, SHAZAM, with Ken White's famous computing package, which has been with us since 1977. 

Ken and I go way back. A few years ago I had a post about the background to the SHAZAM package. In that post I explained what the acronym "SHAZAM" stands for. If you check it out you'll see why it's timely for you to know these important historical facts!

And while you're there, take a look at the links to other tales that illustrate Ken's well-known wry sense of humour.

© 2019, David E. Giles

A Permutation Test Regression Example

In a post last week I talked a bit about Permutation (Randomization) tests, and how they differ from the (classical parametric) testing procedure that we generally use in econometrics. I'm going to assume that you've read that post.

(There may be a snap quiz at some point!)

I promised that I'd provide a regression-based example. After all, the two examples that I went through in that previous post were designed to expose the fundamentals of permutation/randomization testing. They really didn't have much "econometric content".

In what follows I'll use the terms "permutation test" and "randomization test" interchangeably.

What we'll do here is to take a look at a simple regression model and see how we could use a randomization test to see if there is a linear relationship between a regressor variable, x, and the dependent variable, y. Notice that I said a "simple regression" model. That means that there's just the one regressor (apart from an intercept). Multiple regression models raise all sorts of issues for permutation tests, and we'll get to that in due course.

There are several things that we're going to see here:

1. How to construct a randomization test of the hypothesis that the regression slope coefficient is zero.
2. A demonstration that the permutation test is "exact". That it, its significance level is exactly what we assign it to be.
3. A comparison between a permutation test and the usual t-test for this problem.
4. A demonstration that the permutation test remains "exact", even when the regression model is mi-specified by fitting it through the origin.
5. A comparison of the powers of the randomization test and the t-test under this model mis-specification.

What is a Permutation Test?

Permutation tests, which I'll be discussing in this post, aren't that widely used by econometricians. However, they shouldn't be overlooked.

Let's begin with some background discussion to set the scene. This might seem a bit redundant, but it will help us to see how permutation tests differ from the sort of tests that we usually use in econometrics.

Background Motivation

When you took your first course in economic statistics, or econometrics, no doubt you encountered some of the basic concepts associated with testing hypotheses. I'm sure that the first exposure that you had to this was actually in terms of "classical", Neyman-Pearson, testing. 

It probably wasn't described to you in so many words. It would have just been "statistical hypothesis testing". The whole procedure would have been presented, more or less, along the following lines:

Some April Reading for Econometricians

Here are my suggestions for this month:

• Hyndman, R. J., 2019. A brief history of forecasting competitions. Working Paper 03/19, Department of Econometrics and Business Statistics, Monash University.
• Kuffner, T. A. & S. G. Walker, 2019. Why are p-values controversial?. American Statistician, 73, 1-3.
• Sargan, J. D.,, 1958. The estimation of economic relationships using instrumental variables. Econometrica, 26, 393-415. (Read for free online.)  
• Sokal, A. D., 1996. Transgressing the boundaries: Towards a trasnformative hermeneutics of quantum gravity. Social Text, 46/47, 217-252.
• Zeng, G. & Zeng, E., 2019. On the relationship between multicollinearity and separation in logistic regression. Communications in Statistics - Simulation and Computation, published online.
• Zhang, X., S. Paul, & Y-G. Yang, 2019. Small sample bias correction or bias reduction? Communications in Statistics - Simulation and Computation, published online.

© 2019, David E. Giles

Infographics Parades

When I saw Myko Clelland's tweet this morning, my reaction was "Wow! Just, wow!"

Myko (@DapperHistorian) kindly pointed me to the source of this photo that he tweeted about:

It appears on page 343 of Willard Cope Brinton's book, Graphic Methods for Presenting Facts (McGraw-Hill, 1914).

Myko included a brief description in his tweet, but let me elaborate by quoting from pp.342-343 of Brinton's book, and you'll see why I liked the photo so much:

"Educational material shown in parades gives an effective way for reaching vast numbers of people. Fig. 238 illustrates some of the floats used in presenting statistical information in the municipal parade by the employees of the City of New York, May 17, 1913. The progress made in recent years by practically every city department was shown by comparative models, charts, or large printed statements which could be read with ease fro either side of the street. Even though the day of the parade was rainy, great crowds lined the sidewalks. There can be no doubt that many of the thousands who saw the parade came away with the feeling that much is being accomplished to improve the conditions of municipal management. A great amount of work was necessary to prepare the exhibits, but the results gave great reward."

Don't you just love it? A gigantic mobile poster session!

© 2019, David E. Giles

A World Beyond p < 0.05

The American Statistical Association has just published a special supplementary issue of The American Statistician, titled Statistical Inference in the 21st. Century: A World Beyond p < 0.05.

This entire issue is open-access. In addition to an excellent editorial, Moving to a World Beyond "p < 0.05" (by Ronald Wasserstein, Allen Schirm, and Nicole Lazar) it comprises 43 articles with such titles as:

• The p-Value Requires Context, Not a Threshold (by Rebecca Betensky)
• The False Positive Risk: A Proposal Concerning What to do About p-Values (by David Colquhoun)
• What Have we (Not) Learnt From Millions of Scientific Papers With P Values? (by John Ioannidis)
• Three Recommendations for Improving the Use of p-Values (by Daniel Benjamin and James Berger)

I'm sure that you get the idea of what this supplementary issue is largely about.

But look back at its title - Statistical Inference in the 21st. Century: A World Beyond p < 0.05. It's not simply full of criticisms. There's a heap of excellent, positive, and constructive material in there.

Highly recommended reading!

© 2019, David E. Giles

The 2019 Econometric Game

The annual World Championship of Econometrics, The Econometric Game, is nearly upon us again!

Readers of this blog will be familiar with "The Game" from posts relating to this event in previous years. For example, see here for some 2018 coverage.

This year The Econometric Game will be held from 10 to 12 April. As usual, it is being organized by the study association for Actuarial Science, Econometrics & Operational Research (VSAE) of the University of Amsterdam. 

Teams of graduate students from around the globe will be competing for top prize on the basis of their analysis of econometrics case studies. The top three tams in 2018 were from  Universidad Carlos III Madrid,  Harvard University, and Aarhus University.

Check out this year's Game, and I'll post more on it next month.

(30 March, 2019 update - This year's theme has now been announced. It's "Climate Econometrics".)

© 2019, David E. Giles