No Pressure Here

This post might make me sound a little grumpy. I hope not. Anyway, here goes.

Comments that are posted on this blog come to me by email for "approval" prior to posting. This is standard practice, and believe me, you wouldn't want t see some of the spam that people try to post as "comments".

Among the comments waited to be vetted this morning were two at opposite ends of the non-spam spectrum.

One was a grateful and thoughtful comment from "Tom" on my post, ARDL Models - Part I . Here's the exchange in full:

Research on the Interpretation of Confidence Intervals

Like a lot of others, I follow Andrew Gelman's blog with great interest, and today I was especially pleased to see this piece relating to a recent study on the extent to which researchers do or do not interpret confidence intervals correctly.

If you've ever taught an introductory curse on statistical inference (from a frequentist, rather than Bayesian perspective), then I don't need  to tell you how difficult it can be for students to really understand what a confidence interval is, and (perhaps more importantly) what it isn't!

It's not only students who have this problem. Statisticians acting as "expert witnesses" in court cases have no end of trouble getting judges to understand the correct interpretation of a confidence interval. And I'm sure we've all seen or heard empirical researchers misinterpret confidence results! For a specific example of the latter, involving a subsequent Nobel laureate, see my old post here!

The study that's mentioned by Andrew today was conducted by four psychologists (Hoekstra et al., 2014) and involved a survey of academic psychologists at three European Universities. The participants included 442 Bachelor students, 34 Master students, and 120 researchers (Ph.D. or faculty members).

Yes, the participants in this survey are psychologists, but we won't hold that against them, and my hunch is that if we changed "psychologist" to "economist" the results wouldn't alter that much!

Before summarizing the findings of this study, let's see what the authors have to say about the correct interpretation of a confidence interval (CI) constructed from a particular sample of data:

Seminars by the Number - Redux

In my second post on this blog, just over three years ago, I took a shot at seminars - economics seminars in particular. There's nothing there that I want to retract. I still remain bemused by the duration of economics seminars; the time that's wasted on details rather than "the big picture"; and the proportion of the allotted time that's taken up with audience "participation".

This being the case, I thought I'd update my earlier suggestion for streamlining these seminars. The focus is on seminars of an econometric nature - very occasionally we actually do have such events in my department.

Here's what I suggested in that earlier post:

Testing for Multivariate Normality

In a recent post I commented on the connection between the multivariate normal distribution and marginal distributions that are normal. Specifically, the latter do not necessarily imply the former.

So, let's think about this in terms of testing for normality.

Suppose that we have several variables which we think may have a joint distribution that's normal. We could test each of the variables for normality, separately, perhaps using the Jarque-Bera LM test. If the null hypothesis of normality was rejected for one or more of the variables, this could be taken as evidence against multivariate normality. However, if normality couldn't be rejected for any of the variables, this wouldn't tell us anything about their joint distribution.

What we need is a test for multivariate normality itself. Let's see what's available.

March Madness in the Reading Department

It's time for the monthly round-up of recommended reading material.

• Gan, L. and J. Jiang, 1999. A test for global maximum. Journal of the American Statistical Association, 94, 847-854.
• Nowak-Lehmann, F., D. Herzer, S. Vollmer, and I. Martinez-Zarzosa, 2006. Problems in applying dynamic panel data models: Theoretical and empirical findings. Discussion Paper Nr. 140, IAI, Georg-August-Universität Göttingen.
• Olive, D. J., 2004. Does the MLE maximize the likelihood? Mimeo., Department of Mathematics, Southern Illinois University. 
• Pollock, D. S. G., 2014. Econometrics: An historical guide for the uninitiated. Working Paper No. 14/05, Department of Economics, University of Leicester.
• Terrell, G. R., 2002. The gradient statistic. Interface 2002: Computing Science and Statistics, Vol. 34.
• Wald, A., 1940. The fitting of straight lines if both variables are subject to error. Annals of Mathematical Statistics, 11, 284-300.

© 2014, David E. Giles

The Normality of Joint and Marginal Distributions

I'm often surprised how many people are confused when it comes to joint and marginal normal distributions.

Most students of econometrics are taught that the marginal and conditional distributions associated with a multivariate normal random vector are themselves normal. That is, if

         p(x₁, x₂, ...., x_n) ~ MVN[μ₁, ....., μ_n ; V]              ;      where V = {v_ij}

then
         p(x_i) ~ N[μ_i ; v_ii]  .

Similarly, p(x₁ | x₂, x₃, ...., x_n), and all of the other conditional densities are normal.

However, what they don't seem to get taught is that the converse is not true. That is, if we have several random variables, each with normal marginal distributions, then the joint distribution of these variables is not necessarily normal.

It all depends on what copula is used to construct the joint distribution.


© 2014, David E. Giles

Arnold's "Signature"

Anonymity is part of the culture when it comes to refereeing papers submitted for possible publication in economics, econometrics, and statistics. Referees' names are typically "blinded", and some journals use a "double-blind" process, so that authors names are not know by the referees. Not all disciplines use this approach.

The double-blind approach is far from perfect, especially given how easy it often is to identify authors  by locating a "working paper" version of their article through an internet search. In addition, referees often effectively "reveal" their identity by insisting that authors include references to the referee's own work.

Sometimes, though, referees expose themselves quite unwittingly. Here's a case in point. 

Off to New Zealand in July

The New Zealand Association of Economists is holding its 55^th annual conference in early July of this year, in Auckland.

I'm delighted that I'll be there as a keynote speaker. 

The very first conference presentation that I made was at the meeting of the NZAE, in Palmerston North, in 1972. I'm very grateful to be participating this year!

© 2014, David E. Giles

Happy Birthday Sir Ronald Fisher

Ronald Aylmer Fisher.

Born: 17 February, 1890, in East Finchley, London, England 

Knighted: 1952

Other major Honours: Fellow of the Royal Society (1929), Royal Medal (1938), Guy Medal in Gold (1947), Copley Medal (1956), Darwin-Wallace Medal (1958)

Died: 29 July 1962, in Adelaide, S.A., Australia

If you're a student of Econometrics, think of:

• Maximum likelihood estimation
• Fisher's information
• Analysis of variance
• Sampling distributions (for various statistics)
• The null hypothesis
• The F distribution (sort of)

Some previous related posts:

• And in the Red Corner.....
• A Bayesian and Non-Bayesian Marriage
• On the Importance of Gong Global
• Whose F Distribution Was It?

The Fisher digital archives are housed in the University of Adelaide Library.


© 2014, David E. Giles

Sir Francis Galton

Sir Francis Galton, who gave us the concepts of both correlation, and regression, was born on this day, 16 February, in 1822. Galton was one of the great "polymaths" - he had a finger in every pie he could find - as is described in his Wikipedia entry.

We him a debt of gratitude for the role he played in The Origin of our Species.

It's a busy birthday month, with more to follow tomorrow!

© 2014, David E. Giles