The Cauchy Estimator & Unit Root Tests

As we all know, there's more than one way to estimate a regression equation. Some of the estimators that we frequently use include OLS, GLS, IV, GMM, LAD, and ML. Some of these estimators are special cases of some of the others, depending on the circumstances.

But have you ever used the Cauchy estimator? Probably not, even though it's been around (at least) since 1836.

Visualization Methods

Data visualization is an important part of any statistical analysis, including econometric modelling. This is a point I've made before, I know (here, for example). However, it's worth repeating the message from time to time. The Visual-Literacy website has a fun item that summarizes some of the different ways of conveying information in a visual manner: Periodic Table of Visualization Methods.

To be sure, not all of them are relevant to econometricians, but I thought it was kinda fun!

(H-T to John Cook and his @StatFact)

© 2012, David E. Giles

Topp-Leone Distribution

In May, I posted about bias-correcting maximum likelihood estimators (MLEs), and I referred to a series of related papers that I've been authoring/co-authoring in recent times.

I've just completed another such paper - this one relates to the estimation of the scale parameter in the so-called Topp-Leone (1955) distribution. You can access the paper here; and the abstract explains why this distribution is especially interesting, and summarizes the main results:

"The Topp-Leone distribution is attractive for reliability studies as it has finite support and a bathtub-shaped hazard function. We compare some properties of the method of moments, maximum likelihood, and bias-adjusted maximum likelihood estimators of its shape parameter. The last of these estimators is very simple to apply and dominates the method of moments estimator in terms of relative bias and mean squared error."

Economic Forecasting

I really enjoyed this post, titled Economic Forecasting: Is Google Trends the Future?, by Livio Di Matteo, on the Worthwhile Canadian Initiative blog.

The title speaks for itself.

© 2012, David E. Giles

"The Rise of Econometrics"

Readers of this blog will know that I have an (untrained) interest in the history of econometrics.

Even so, I'm afraid I don't see myself spending $1,300 to buy the set of volumes going by the name of this post's title, when Routledge publishes it in December!

 

Edited by Duo Qin, you'll get 1,777 pages, and:

"The set provides an authoritative one-stop resource to enable users to understand what has shaped econometrics into its current form. With a full index and comprehensive introductions to each volume, newly written by the editor, the collection also provides a synoptic view of many current key debates and issues."
 

 Hopefully I can persuade the UVic Library to get on board!

 

In any case, the Table of Contents for this 4-volume set provides a fine reading guide for serious students of econometrics. Take a look, and then do some bedtime reading!

 

© 2012, David E. Giles

On Becoming a Sportsmetrician

Wouldn't you know it!? No sooner had I posted about Analysing Olympic Medal Data than the latest issue of AmstatNews hit my (snail) mailbox. AmstatNews is the monthly magazine for members of the American Statistical Association.

In the STATtr@ck section, there's a nice article by Jim Albert, titled "Preparing for a Career as a Sports Statistician: Two Interviews With People in the Field".

Take a look if you have any inclination of  becoming a Sportsmetrician.

© 2012, David E. Giles

Analysing Olympic Medal Data

So, the London Olympics are over - with the Paralympics still to come, of course. Sports, and events such as the Olympic Games, generate lots of lovely data. It's also usually "hard" data. So, there's a cottage industry out there comprised of statisticians of all shapes and forms who love to work sports data.

The American Statistical Association has a Section for Statistics in Sport, publishes the Journal of Quantitative Analysis in Sports, and provides access to some interesting sports data-sets.

Interview With George Judge

The journal, Econometric Theory, has a long-standing tradition of publishing excellent interviews with econometricians (and some statisticians) who have made seminal contributions to our discipline over the years.

This has always struck me as a particularly worthwhile service to the econometrics community, and I often encourage my grad. students to read these interviews.

In an ET Interview that will be appearing shortly, Anil Bera talks to George Judge. Anil has made a copy of the interview available here, and I think that it will be of considerable interest to many readers.

© 2012, David E. Giles

Whose F Distribution Was It?

We use the F-distribution all of the time in our econometric work. But why is it called the "F" distribution?

A lot of students guess that the name is related to the great statistician, Sir Ronald A. Fisher. They're partly right. However, the occasionally encountered term, "Fisher's F Distribution" is somewhat misleading. The alternative terms, "Snedecor's F distribution" or the "Fisher-Snedecor Distribution" offer more accurate information.

Personally, I prefer to call it "Snedecor's F" - after George W. Snedecor. Here's why.

Egon Pearson

During the last few days, the Error Statistics blog has included posts about Egon Sharpe Pearson. Egon (son of Sir Karl Pearson), made numerous fundamental contributions to mathematical statistics, many of which bear directly on the development and practice of econometrics.

I had a post about the Neyman-Pearson Lemma earlier this year.

Goodness-of-Fit Testing With Discrete "Circular" Data

Tests for goodness-of-fit based on the empirical distribution function are pretty standard fare. Their applicability relies on the Glivenko-Cantelli Theorem.

However, things get a little tricky when the data are discrete (rather than continuous), or when they are "circular" in nature. When the data exhibit both of these characteristics, some really interesting testing issues have to be handled.

A paper that I wrote a short while back on this topic has just been accepted for publication in the Chilean Journal of Statistics. The paper is titled, "Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications", and it'll be appearing in the 2013 volume of the journal.

You can download  a copy of the paper here.

 

© 2012, David E. Giles

The Likelihood Principle

The so-called "Likelihood Principle" forms the foundation of both classical (frequentist) statistics, as well as Bayesian statistics. So, as an econometrician, whether you rely on Maximum Likelihood estimation and the associated asymptotic tests, or if you prefer to adopt a Bayesian approach to inference, this principle is of fundamental importance to you.

What is this principle? Suppose that x is the value of a (possibly vector-valued) random variable, X, whose density depends on a vector of parameters, θ. Then, the Likelihood Principle states that:

"All the information about θ obtainable from an experiment is contained in the likelihood function for θ given x. Two likelihood functions for θ (from the same or different experiments) contain the same information about θ if they are proportional to one another."  (Berger and Wolpert, 1988, p.19).

Promoting Econometrics

A post today on the "Simply Statistics" blog is titled, "Statistics/Statisticians Need Better Marketing". 

I liked it a lot, and much of the content could be applied to the econometrics community. 

However, one of the suggestions worried me a bit - namely:

"Whenever someone does something with data, we should claim them as a statistician."

I'm not sure I'd like to claim as an econometrician, anyone who does some empirical analysis involving economic data. Goodness knows there's an awful lot of garbage out there! And it's produced by people I wouldn't call econometricians, even if that's how they describe tehmselves!

But maybe I'm just getting old and grumpy.

© 2012, David E. Giles

Videos on Using R

In this post on his blog some months ago, Ethan Fosse drew attention to Anthony Damico's collection of over 90 videos on using the R software environment.

Definitely worth looking at!

© 2012, David E. Giles

International Year of Statistics

2013 will be The International Year of Statistics. The associated website can be found here.

Quoting from the site:

"The International Year of Statistics ("Statistics2013") is a worldwide celebration and recognition of the contributions of statistical science. Through the combined energies of organizations worldwide, Statistics2013 will promote the importance of Statistics to the broader scientific community, business and government data users, the media, policy makers, employers, students, and the general public. 

The goals of Statistics2013 include: 

• increasing public awareness of the power and impact of Statistics on all aspects of society;
• nurturing Statistics as a profession, especially among young people; and
• promoting creativity and development in the sciences of Probability and Statistics"

Various upcoming activities that acknowledge the International Year of Statistics can be found here.

© 2012, David E. Giles

James Durbin

James Durbin has passed away at the age of 89. Jim's numerous contributions to statistics included many that also made him a "household name" in econometrics circles.

There is a short obituary on p.7. of the latest issue of RSS News. A full obituary will follow in a future issue of The Journal of the Royal Statistical Society, Series A.

For some earlier historical material relating to James Durbin in this blog, see the earlier post here.

© 2012, David E. Giles