Back to School Reading

Here we are - it's Labo(u)r Day weekend already in North America, and we all know what that means! It's back to school time.

You'll need a reading list, so here are some suggestions:

• Frances, Ph. H. B. F., 2019. Professional forecasters and January. Econometric Institute Research Papers EI2019-25, Erasmus University Rotterdam.
• Harvey, A. & R. Ito, 2019. Modeling time series when some observations are zero. Journal of Econometrics, in press.
• Leamer, E. E., 1978. Specification Searches: Ad Hoc Inference With Nonexperimental Data. Wiley, New York. (This is a legitimate free download.)
• MacKinnon, J. G., 2019. How cluster-robust inference is changing applied econometrics. Working Paper 1413, Economics Department, Queen's University.
• Steel, M. F. J., 2019. Model averaging and its use in economics. Mimeo., Department of Statistics, University of Warwick.
• Stigler, S. M., 1981. Gauss and the invention of least squares. Annals of Statistics, 9, 465-474. 

© 2019, David E. Giles

Including More History in Your Econometrics Teaching

If you follow this blog (or if you look at the "History of Econometrics" label in the word cloud in the right side-bar), you'll know that I have more than a passing interest in the history of our discipline. There's so much to be learned from this history. Among other things, we can gain insights into why certain methods became popular, and we can reduce the risk of repeating earlier mistakes!

When I was teaching I liked to inject a few historical facts/anecdotes/curiosities into my classes. I think that this brought the subject matter to life a little. The names behind the various theorems, tests, and estimators are those of real people, after all.

There are some excellent books on the history of econometrics, including those by Epstein (1987), Morgan (1990), and De Marchi and Gilbert (1991). (Also, see the short piece by Stephen Pollock, 2014.)

However, I think that we could do more in terms of making material about this history accessible to our students.

The Statistics community has gone much further in this direction, and we might take note of this.

The other day, Amanda Golbeck posted some very helpful links on the American Statistical Association's "History of Statistics Interest Group" community noticeboard.

Here's her posting in its entirety - and don't miss the first of her links:

"Why not include more history in your teaching? The History of Statistics Interest Group library has a collection of Activities for Classes: community.amstat.org/historyofstats/ourlibrary/...

We are pleased to let you know that Bob Rosenfeld has created 13 history of probability and statistics teaching modules, and he has kindly made them available for you to use in your classes! We hope you will find them to be useful.

Reading and Exercises on the History of Probability from the Vermont Mathematics Initiative, Bob Rosenfeld

• Pre-history to 1600 (PDF)
• 17th Century France (PDF)
• Jacob Bernoulli - Law of Large Numbers (PDF)
• Inverse Probability - Thomas Bayes (PDF)
• Laplace (PDF)

Reading and Exercises on the History of Statistics from the Vermont Mathematics Initiative, Bob Rosenfeld

• John Graunt and the Bills of Mortality (PDF)
• Origin of the Normal Curve (PDF)
• Origins of Graphs in Statistics (PDF)
• Fitting models to data - the Path to Least Squares (PDF)
• Statistics Moves from Physical to Social Sciences (PDF)
• Correlation - Francis Galton (PDF)
• t-Distribution and Gosset (PDF)
• Fisher and Design of Experiments (PDF)"

(Bob Rosenfeld was former Co-Director for Statistics and School-Based Research at the Vermont Mathenatics initiative, and the author of a number of books on the teaching of statistics to K-8 students. D.G.)

Most of Bob Rosenfeld's pieces are directly relevant to econometrics students. It would be nice to see more material about the history of our discipline that could be incorporated into introductory econometrics courses.

References 

De Marchi, N. & C. Gilbert, 1990. History and Methodology of Econometrics. Oxford University Press, Oxford.

Epstein, R. J. 1987. A History of Econometrics. North-Holland, Amsterdam.

Morgan, M. S., 1991. The History of Econometric Ideas. Cambridge University Press, Cambridge.

Pollock, D. S. G., 2014. Econometrics - An historical guide for the uninitiated. Working Paper No. 14/05, Department of economics, University of Leicester.

© 2019, David E. Giles

Suggested Reading for August

Here are my suggestions for this month:

• Bun, M. J. G. & T. D. Harrison, 2109. OLS and IV estimation of regression models including endogenous interaction terms. Econometric Reviews, 38, 814-827.
• Dufour, J-M., E. Flachaire, & L. Khalaf, Permutation tests for comparing inequality measures. Journal of Business and Economic Statistics, 37, 457-470.
• Jiao, X. & F. Pretis, 2018. Testing the presence of outliers in regression models. Available at SSRN: https://ssrn.com/abstract=3217213.
• Stanton, J. M., 2001. Galton, Pearson, and the peas: A brief history of linear regression for statistics instructors. Journal of Statistics Education, 9, 1-13.
• Trafimow, D., 2019. A frequentist alternative to significance testing, p-values and confidence intervals. Econometrics, 7, 26.

© 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

Bradley Efron and the Bootstrap

Econometricians make extensive use of various forms of "The Bootstrap", thanks to Bradley (Brad) Efron's pioneering work.

I've posted about the history of the bootstrap previously - e.g., here, and here.

You probably know by now that Brad was awarded The International Prize in Statistics last November - this was only the second time that this prize has been awarded. It's difficult to think of a more deserving recipient.

If you want to read an excellent account of Brad's work, and how the bootstrap came to be, I recommend the 2003 piece by Susan Holmes, Carl Morris, and Rob Tibshirani.

There are some fascinating snippets in this conversation/interview, including:

Efron: "One of the reasons I came to Stanford was because of its humor magazine. I wrote a humor column at Caltech, and I always wanted to write for a humor magazine. Stanford had a great humor magazine, The Chaparral. The first few months I was there, the editor literally went crazy and had to be hospitalized, and so I became editor. For one issue we did a parody of Playboy and it went a little too far. I was expelled from school, ..... I went away for 6 months and then I came back. That was by far the most famous I’ve ever been." 

 Referring to his seminal paper (Efron, 1979):

Tibshirani: "It was sent to the Annals. What kind of reception did it get?" 

Efron: "Rupert Miller was the editor of the Annals at the time. I submitted what was the Rietz lecture, and it got turned down. The associate editor, who will remain nameless, said it that didn’t have any theorems in it. So, I put some theorems in at the end and put a lot of pressure on Rupert, and he finally published it."

I guess there's still hope for the rest of us!

References

Efron, B., 1979. Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1-26.

Holmes, S., C. Morris, & R. Tibshirani, 2003. Bradley Efron: A conversation with good friends. Statistical Science, 18, 268-281.

© 2019, David E. Giles

Recommended Reading

Here's my reading list for August:

• Ardia, D., K. Bluteau, & L. F. Hoogerheide, 2018. Methods for computing numerical standard errors: Review and application to value-at-risk estimation. Journal of Time Series Econometrics. Available online.
• Bauer, D. & A. Maynard, 2012. Persistence-robust surplus-lag Granger causality testing. Journal of Econometrics, 169. 293-300.
• David, H. A., 2009. A historical note on zero correlation and independence. American Statistician, 63, 185-186.
• Fisher, T. J. & M. W. Robbins, 2018. A cheap trick to improve the power of a conservative hypothesis tests. American Statistician. Available online.
• Granger, C. W. J., 2012. Useful conclusions from surprising results. Journal of Econometrics, 169, 142-146.
• Harville, D. A., 2014. The need for more emphasis on prediction: A 'nondenominational' model-based approach (with discussion). American Statistician, 68, 71-92.

© 2018, David E. Giles

My August Reading List

Here are some suggestions for you:

• Calzolari, G., 2017. Econometrics exams and round numbers: Use or misuse of indirect estimation methods? Communications in Statistics - Simulation and Computation, in press.
• Chakraborti, S., F. Jardim, & E. Epprecht, 2017. Higher order moments using the survival function: The alternative expectation formula. American Statistician, in press.
• Clarke, J. A., 2017. Model averaging OLS and 2SLS: An application of the WALS procedure. Econometrics Working Paper EWP1701, Department of Economics, University of Victoria.
• Hotelling, H., 1940. The teaching of statistics, Annals of Mathematical Statistics, 11, 457-470.
• Knaeble, B. & S. Dutter, 2017. Reversals of least-square estimates and model-invariant estimation for directions of unique effects. American Statistician, 71, 97-105.
• Megerdichian, A., 2017. Further results on interpreting coefficients in regressions with a logarithmic dependent variable. Journal of Econometric Methods, in press.

© 2017, David E. Giles

New Year's Reading

New Year's resolution - read more Econometrics!

• Bürgi, C., 2016. What do we lose when we average expectations? RPF Working Paper No. 2016-013, Department of Economics, George Washington University.
• Cox, D.R., 2016. Some pioneers of modern statistical theory:A personal reflection. Biometrika, 103, 747-759
• Golden, R.M., S.S. Henley, H. White, & T.M. Kashner, 2016. Generalized information matrix tests for detecting model misspecification. Econometrics, 4, 46; doi:10.3390/econometrics4040046.
• Phillips, G.D.A. & Y. Xu, 2016. Almost unbiased variance estimation in simultaneous equations models. Working Paper No. E2016/10, Cardiff Business School, University of Cardiff. 
• Siliverstovs, B., 2016. Short-term forecasting with mixed-frequency data: A MIDASSO approach. Applied Economics, 49, 1326-1343.
• Vosseler, A. & E. Weber, 2016. Bayesian analysis of periodic unit roots in the presence of a break. Applied Economics, online.

Best wishes for 2017, and thanks for supporitng this blog!

© 2016, David E. Giles

Stephen E. Fienberg, 1942-2016

The passing of Stephen Fienberg today is another huge loss for the statistics community. Carnegie Mellon University released this obituary this morning.

Steve was born and raised in Toronto, and completed his undergraduate training in mathematics and statistics at the University of Toronto before moving to Harvard University for his Ph.D.. His contributions to statistics, and to the promotion of statistical science, were immense.

As the CMU News noted:

"His many honors include the 1982 Committee of Presidents of Statistical Society President's Award for Outstanding Statistician Under the Age of 40; the 002 ASA Samuel S. Wilks Award for his distinguished career in statistics; the first Statistical Society of Canada's Lise Manchester Award in 2008 to recognize excellence in state-of-the-art statistical work on problems of public interest; the 2015 National Institute of Statistical Sciences Jerome Sacks Award for Cross-Disciplinary Research; the 2015 R.A. Fisher Lecture Award from the Committee of Presidents of Statistical Societies and the ISBA 2016 Zellner Medal. 

Fienberg published more than 500 technical papers, brief papers, editorials and discussions.  He edited 19 books, reports and other volumes and co-authored seven books, including 1999's "Who Counts? The Politics of Census-Taking in Contemporary America," which he called "one of his proudest achievements." " 

There at least three terrific interviews with Steve that we have to remind us of the breadth of his contributions:

• Interview With Steve Fienberg, by Sam Behseta and Aleksandra Slavkovic.
• A Conversation With Stephen E. Fienberg, by Miron Straf and Judith Tanur.
• "In most places, not only are statisticians not in control of Big Data efforts and data science, but sometimes they are totally excluded or at best, marginalised." An interview with Stephen Fienberg, in Statistics Views.

© 2016, David E. Giles

Monte Carlo Simulation Basics, I: Historical Notes

Monte Carlo (MC) simulation provides us with a very powerful tool for solving all sorts of problems. In classical econometrics, we can use it to explore the properties of the estimators and tests that we use. More specifically, MC methods enable us to mimic (computationally) the sampling distributions of estimators and test statistics in situations that are of interest to us. In Bayesian econometrics we use this tool to actually construct the estimators themselves. I'll put the latter to one side in what follows.

T. W. Anderson: 1918-2016

Unfortunately, this post deals with the recent loss of one of the great statisticians of our time - Theodore (Ted) W. Anderson.

Ted passed away on 17 September of this year, at the age of 98.

I'm hardly qualified to discuss the numerous, path-breaking, contributions that Ted made as a statistician. You can read about those in De Groot (1986), for example.

However, it would be remiss of me not to devote some space to reminding readers of this blog about the seminal contributions that Ted Anderson made to the development of econometrics as a discipline. In one of the "ET Interviews", Peter Phillips talks with Ted about his career, his research, and his role in the history of econometrics.  I commend that interview to you for a much more complete discussion than I can provide here.

(See this post for information about other ET Interviews).

Ted's path-breaking work on the estimation of simultaneous equations models, under the auspices of the Cowles Commission, was enough in itself to put him in the Econometrics Hall of Fame. He gave us the LIML estimator, and the Anderson and Rubin (1949, 1950) papers are classics of the highest order. It's been interesting to see those authors' test for over-identification being "resurrected" recently by a new generation of econometricians. 

There are all sorts of other "snippets" that one can point to as instances where Ted Anderson left his mark on the history and development of econometrics.

For instance, have you ever wondered why we have so many different tests for serial independence of regrsssion errors? Why don't we just use the uniformly most powerful (UMP) test and be done with it? Well, the reason is that no such test (against the alternative of a first-oder autoregresive pricess) exists.

That was established by Anderson (1948), and it led directly to the efforts of Durbin and Watson to develop an "approximately UMP test" for this problem.

As another example, consider the "General-to-Specific" testing methodology that we associate with David Hendry, Grayham Mizon, and other members of the (former?) LSE school of thought in econometrics. Why should we "test down", and not "test up" when developing our models? In other words, why should we start with the most  general form of the model, and then successively test and impose restrictions on the model, rather than starting with a simple model and making it increasingly complex? The short answer is that if we take the former approach, and "nest" the successive null and alternative hypotheses in the appropriate manner, then we can appeal to a theorem of Basu to ensure that the successive test statistics are independent. In turn, this means that we can control the overall significance level for the set of tests to what we want it to be. In contrast, this isn't possible if we use a "Simple-to-General" testing strategy.

All of this spelled out in Anderson (1962) in the context of polynomial regression, and is discussed further in Ted's classic time-series book (Anderson, 1971). The LSE school referred to this in promoting the "General-to-Specific" methodology.

Ted Anderson published many path-breaking papers in statistics and econometrics and he wrote several books - arguably, the two most important are Anderson (1958, 1971). He was a towering figure in the history of econometrics, and with his passing we have lost one of our founding fathers.

References

Anderson, T.W., 1948. On the theory of testing serial correlation. Skandinavisk Aktuarietidskrift, 31, 88-116.

Anderson, T.W., 1958. An Introduction to Multivariate Statistical Analysis. WIley, New York (2nd. ed. 1984).

Anderson, T.W., 1962. The choice of the degree of a polynomial regression as a multiple decision problem. Annals of Mathematical Statistics, 33, 255-265.

Anderson, T.W., 1971. The Statistical Analysis of Time Series. Wiley, New York.

Anderson, T.W. & H. Rubin, 1949. Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics, 20, 46-63.

Anderson, T.W. & H. Rubin, 1950. The asymptotic properties of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics, 21,570-582.

De Groot, M.H., 1986. A Conversation with T.W. Anderson: An interview with Morris De Groot. Statistical Science, 1, 97–105.

© 2016, David E. Giles

International Prize in Statistics

A few days ago, the inaugural winner of the biennial International Prize in Statistics was announced.

The first recipient of the new award is Sir David Cox, whose work is, of course, well known to econometricians.

The award was made to Sir David for his "Survival Analysis Model Applied in Medicine, Science, and Engineering".

September Reading

Here are a few suggestions for some interesting reading this month:

• Esquivel, M.L., P.P. Mota, & J.T. Mexia, 2016. On some statistical  models with a random number of observations. Journal of Statistical Theory and Practice, online.
• Gorroochurn, P., 2015. On Galton's change from "reversion" to "regression". American Statistician, in press.
• Kourtellos, A., T. Stengos, & C.M. Tan, 2016. Structural threshold regression. Econometric Theory, 32,827-860.
• Jandhyala, V., S. Fotopoulos, I. MacNeill, & P. Liu, 2016. Inference for single and multiple change-points in time series. Journal of Time Series Analysis, in press.
• Malloch, H., R. Philip, & S. Satchell, 2016. Decomposing the bias in time-series estimates of CAPM betas. Applied Economics, 28, 4291-4298.
• Xu, J. & P. Perron, 2016. Forecasting in the presence of in and out of sample breaks. Mimeo.

© 2016, David E. Giles

Reading List for October

Some suggestions for the coming month:

• Franses, P. H., 2016. A note on the mean absolute scaled error. International Journal of Forecasting, 32, 20-22.
• Gorroochurn, P., 2015. On Galton's change from 'reversion' to 'regression'. American Statistician, in press.
• Holan, S. H., R. Lund, and G. Davis, 2010. The ARMA alphabet soup: A tour of ARMA model variants. Statistics Surveys, 4, 232-274.
• Liu, S., H. Wu, and W. Q. Meeker, 2015. Understanding and addressing the unbounded "likelihood" problem. American Statistician, 69, 191-200.
• McCracken, M. W. and S. Ng, 2015.  FRED-MD: A monthly database for macroeconomic research. Journal of Business and Economic Statistics, in press.
• Müller, U. K. and M. W. Watson, 2015. Low-frequency econometrics. NBER Working Paper No. 21564.

© 2015, David E. Giles

'Student', on Kurtosis

W. S. Gosset (Student) provided this useful aid to help us remember the difference between platykurtic and leptokurtic distributions:

('Student', 1927. Errors of routine analysis. Biometrika, 19, 151-164. See p. 160.)

Here, β₂ is the fourth standardized moment of the distribution about its mean. The Normal distribution has β₂ = 3.

The appropriate definition of "kurtosis" for uni-modal distributions has been the subject of considerable discussion in the statistical literature. Should it be based on the characteristics of the tail of the distribution; the shape of the density around its mode; or both? 

© 2015, David E. Giles

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 artificial intelligence. However, I hadn't realized the extent of Turing's use of, and contributions to, a range of important statistical tools. Some of these tools have a direct bearing on Econometrics.

For example:

• (HT to Lief Bluck for this one.) In 1935, at the tender age of 22, Turing was appointed a Fellow at King's College, Cambridge, on the basis of his 1934 (undergraduate) thesis in which he proved the Central Limit Theorem. More specifically, he derived a proof of what we now call the Lindeberg-Lévy Central Limit Theorem.  He was not aware of Lindeberg's earlier work (1920-1922) on this problem. Lindeberg, in turn, was unaware of Lyapunov's earlier results. (Hint: there was no internet back then!). How many times has your econometrics instructor waved her/his arms and muttered ".......as a result of the central limit theorem....."?
• In 1939, Turing developed what Wald and his collaborators would later call "sequential analysis". Yes, that's Abraham Wald who's associated with the Wald tests that you use all of the time.Turing's wartime work on this subject remained classified until the 1980's. Wald's work became well-established in the literature by the late 1940's, and was included in the statistics courses that I took as a student in the 1960's. Did I mention that Wald's wartime associates included some familiar names from economics? Namely, Trygve Haavelmo, Harold Hotelling, Jacob Marschak, Milton Friedman, W. Allen Wallis, and Kenneth Arrow.
• The mathematician/statistician I. J. ("Jack") Good was a member of Turing's team at Bletchley Park that cracked the Enigma code. Good was hugely influential in the development of modern Bayesian methods, many of which have found their way into econometrics. He described the use of Bayesian inference in the Enigma project in his "conversation" with Banks (1996). (This work also gave us the Good-Turing estimator - e.g., see Good, 1953.)
• Turing (1948) devised the LU ("Lower and Upper") Decomposition that is widely used for matrix inversion and for solving systems of linear equations. Just think how many times you invert matrices when you're doing your econometrics, and how important it is that the calculations are both fast and accurate!

Added, 20 February, 2015: I have recently become aware of Good (1979)

References

Banks, D. L., 1996. A conversation with I. J. Good. Statistical Science, 11, 1-19.

Good, I. J., 1953.The population frequencies of species and the estimation of population parameters. Biometrika, 40, 237-264.

Good, I. J., 1979. A. M. Turing's statistical work in World War II. Biometrika, 66, 393-396.

Turing, A. M., 1948. Rounding-off errors in matrix processes. Quarterly Journal of Mechanics and Applied Mathematics, 1, 287-308.

© 2014, David E. Giles

Recent Reading

From my "Recently Read" list:

• Born, B. and J. Breitung, 2014. Testing for serial correlation in fixed-effects panel data models. Econometric Reviews, in press.
• Enders, W. and Lee. J., 2011. A unit root test using a Fourier series to approximate smooth breaks, Oxford Bulletin of Economics and Statistics, 74, 574-599.
• Götz, T. B. and A. W. Hecq, 2014. Testing for Granger causality in large mixed-frequency VARs. RM/14/028, Maastricht University, SBE, Department of Quantitative Economics.
• Kass, R. E., 2011. Statistical inference: The big picture. Statistical Science, 26, 1-9.
• Qian, J. and L. Su, 2014. Structural change estimation in time series regressions with endogenous variables. Economics Letters, in press.
• Wickens, M., 2014. How did we get to where we are now? Reflections on 50 years of macroeconomic and financial econometrics. Discussion Paper No. 14/17, Department of Economics and Related Studies, University of York.

© 2014, David E. Giles

Early Computing

During a recent visit to Harvard U. I came across this monstrosity thing of beauty in the Science Center - the building where the Dept. of Statistics is housed:

It's an "Aiken-IBM Automatic Sequence Controlled Calculator - I", and dates from 1944. (Obviously, those other people in the picture liked it a lot too - I couldn't get them out of the way! But they do give you a sense of scale.)

From left to right, the main components of the calculator are:

1. Panel of 60 constants.
2. Unit of 72 storage counters.
3. The multiply/divide unit.
4. Fractional counters.
5. Interpolators - 1, 2, 3.
6. Sequence control.
7. Typewriters (barely visible).
8. Card feed (out of sight).
9. Card punch (even more out of sight!).

It's about the size of strech limo, and a great piece of computing history.

It reminded me of "The Monkey Run" - ah, those were the days!

© 2014, David E. Giles

The 7 Pillars of Statistical Wisdom

Yesterday, Stephen Stigler presented the (ASA) President's Invited Address to an overflow, and appreciative, audience at the 2014 Joint Statistical Meetings in Boston. The title of his talk was, "The Seven Pillars of Statistical Wisdom".

I'd been looking forward to this presentation by our foremost authority on the history of statistics, and it surpassed my (high) expectations.

The address will be published in JASA at some future date, and I urge you to read it when it appears. In the meantime, here are the "seven pillars" - the supporting pillars of statistical science - with some brief comments: