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Matrices, Statistics and Big Data
IWMS, Funchal, Portugal, June 2016
Editors: S. Ejaz Ahmed, Brock University, St. Catharines, Ontario, Canada
Francisco Carvalho, Polytechnic Institute of Tomar, Portugal
Simo Puntanen, University of Tampere, School of Information Sciences, Finland
Table of Contents [00] S. Ejaz Ahmed, Francisco Carvalho and Simo Puntanen 1 page Preface [01] Francisco Carvalho, Simo Puntanen, George P. H. Styan 5 pages Report on The 25th International Workshop on Matrices and Statistics: IWMS-2016, Funchal, Madeira (Portugal): 6–9 June 2016 [02] Augustyn Markiewicz, Simo Puntanen 21 pages Further properties of the linear sufficiency in the partitioned linear model [03] Ivo Sousa-Ferreira, Ana Maria Abreu 10 pages Hybrid model for recurrent event data [04] Radosław Kala 15 pages A new look at combining information from stratum submodels [05] Simo Puntanen, George P. H. Styan 12 pages Ingram Olkin (1924–2016): An Appreciation for a People Person [06] Mika Mattila, Pentti Haukkanen 14 pages A notion of positive definiteness for arithmetical functions [07] George P. H. Styan, Walter Trump, Ka Lok Chu 31 pages Two sensational magic squares and two philatelic magic-carpet dinner-placemats [08] Nathan Hin Shun Chu, Ka Lok Chu, George P. H. Styan 25 pages Se-tenant philatelic Machin-de�nitive blocks with selected total face-values [09] George P. H. Styan, Ka Lok Chu 11 pages An illustrated mini-report on the Madeira Magic Minisymposium “Magic squares, prime numbers and postage stamps” (MMM) at The 25th International Workshop on Matrices and Statistics (IWMS-2016): Funchal, Madeira (Portugal), 6-9 June 2016 [10] Alan Agresti 14 pages Some Issues in Generalized Linear Modeling [11] Sandra S. Ferreira, Dário Ferreira, Célia Nunes, Francisco Carvalho, 9 pages João Tiago Mexia Orthogonal Block Structure and Uniformly Best Linear Unbiased Estimators [12] Carla Francisco, Teresa A. Oliveira, Amílcar Oliveira, Francisco Carvalho 12 pages Hadamard matrices on error detection and correction: Useful links to BIBD [13] Xiangzhao Cui, Zhenyang Li, Jine Zhao, Defei Zhang, Jianxin Pan 14 pages
Covariance Matrix Regularization for Banded Toeplitz Structure via Frobenius-Norm Discrepancy [14] Tao Zhang, Yuan Huang, Qingzhao Zhang, Shuangge Ma, S. Ejaz Ahmed 17 pages Penalized relative error estimation of a partially functional linear multiplicative model [15] S. Ejaz Ahmed, Hwanwoo Kim, Gökhan Yıldırım, Bahadır Yüzbaşı 30 pages High-Dimensional Regression under Correlated Design: An Extensive Simulation Study [16] S. Ejaz Ahmed, Khalifa Es-Sebaiy, Abdulkadir Hussein, Idir Ouassou, 14 pages Anne Snowdon An efficient estimation strategy in autoregressive conditional Poisson model with applications to hospital emergency department data
Prefa eThe 25th International Workshop on Matri es and Statisti s (IWMS-2016)was held in the ity of Fun hal on the beautiful Madeira Island, the Pearl ofthe Atlanti , on 6�9 June 2016.The purpose of this workshop was to bring together resear hers sharingan interest in a variety of aspe ts of statisti s and its appli ations as wellas matrix analysis and its appli ations to statisti s, and to o�er them apossibility to dis uss urrent developments in these subje ts. The workshop ontributed to bridge the gap among statisti ians, omputer s ientists andmathemati ians in understanding ea h other's tools.The Lo al Organizing Committee was haired by Fran is o Carvalho(Tomar, Portugal), and the International Organizing Committee by SimoPuntanen (Tampere, Finland) while George P. H. Styan (Montréal, Québe ,Canada) was the Honorary Chair.IWMS-2016 was organized by Instituto Polité ni o de Tomar and Uni-versidade da Madeira, and was supported by: CMA - Centro de Matemáti ae Apli ações (FCT, UNL), CIMA - Centro de Investigação em Matemáti a eApli ações (UE), PSE - Produtos e Serviços de Estatísti a, INE - InstitutoNa ional de Estatísti a, FLAD - Fundação Luso-Ameri ana para o Desen-volvimento, Delta Cafés, and the Asso iação de Promoção da Madeira.The workshop omprised invited talks, ontributed talks and Spe ial Ses-sions; for the details, see arti le by Carvalho, Puntanen & Styan, appearingin Chapter 1 of this book. The �nal program and the Book of Abstra ts,edited by Daniel Klein & Fran is o Carvalho, are online on the IWMS-2016website.For previous IWMS-workshops, see the IWMS-website, from where, forexample, �A short history of the International Workshop on Matri es andStatisti s� an be downloaded: online pdf. The 26th International Workshopon Matri es and Statisti s will be held in 2018, the venue to be announ ed.This volume, Matri es, Statisti s and Big Data, in the series Pro eedingsin Mathemati s & Statisti s published by Springer Verlag, omprises sele tedrefereed papers presented in the IWMS-2016.We would like to thank all the authors for their valuable ontributionsto this volume. Our spe ial thanks go to all the reviewers for their diligentreviews.May 2017S. Ejaz Ahmed, Fran is o Carvalho & Simo Puntanen, editors.1
[March 29, 2017]
Report onThe 25th International Workshop onMatrices and Statistics: IWMS-2016
Funchal, Madeira (Portugal): 6–9 June 2016
Francisco CarvalhoDepartmental Unit of Mathematics and Physics, Polytechnic Institute of
Tomar and Center of Mathematics and Applications, FCT/UNL,Monte da Caparica, Portugalemail: [email protected]
Simo PuntanenFaculty of Natural Sciences, FI-33014 University of Tampere, Finland
email: [email protected]
George P. H. StyanDepartment of Mathematics and Statistics, McGill University,
Montréal, Québec, Canadaemail: [email protected]
The 25th International Workshop on Matrices and Statistics (IWMS-2016)was held in the city of Funchal on the beautiful Madeira Island, the Pearl ofthe Atlantic, on 6–9 June 2016.
The purpose of this workshop was to bring together researchers sharingan interest in a variety of aspects of statistics and its applications as well asmatrix analysis and its applications to statistics, and to offer them a possi-bility to discuss current developments in these subjects. The workshop willbridge the gap among statisticians, computer scientists and mathematiciansin understanding each other’s tools.
The Local Organizing Committee was chaired by Francisco Carvalho (Tomar,Portugal), with help from Katarzyna Filipiak (Poznań, Poland), Ana MariaAbreu (Madeira, Portugal), and Daniel Klein (Košice, Slovakia).
The International Organizing Committee for the Madeira Workshop com-prised Simo Puntanen (Tampere, Finland) – Chair, George P. H. Styan(Montréal, Québec, Canada) – Honorary Chair, Júlia Volaufová (New Or-leans, Louisiana, USA) – Vice-Chair, S. Ejaz Ahmed (St. Catharines, On-tario, Canada), Katarzyna Filipiak (Poznań, Poland), Jeffrey J. Hunter(Auckland, New Zealand), Augustyn Markiewicz (Poznań, Poland), Dietrichvon Rosen (Uppsala, Sweden), and Hans Joachim Werner (Bonn, Germany).
IWMS-2016 MADEIRA REPORT: March 29, 2017 2
IWMS-2016 was organized by Instituto Politécnico de Tomar and Univer-sidade da Madeira, and was supported by: CMA - Centro de Matemática eAplicações (FCT, UNL), CIMA - Centro de Investigação em Matemática eAplicações (UE), PSE - Produtos e Serviços de Estatística, INE - InstitutoNacional de Estatística, FLAD - Fundação Luso-Americana para o Desen-volvimento, Delta Cafés, and the Associação de Promoção da Madeira.
The invited speakers were
• Alan Agresti (Gainesville, Florida, USA):“Some perspectives about generalized linear modelling”
• Rosemary A. Bailey (St. Andrews, Scotland, UK):“Association schemes in designed experiments”
• Radosław Kala (Poznań, Poland):“A new look at combining information from stratum submodels”
• Alexander Kovačec (Coimbra, Portugal):“The 123 Theorem of probability theory and copositive matrices”
• Jianxin Pan (Manchester, England, UK):“Joint mean-covariance modelling and its R package: jmcm”
A Special Session to Celebrate Jeffrey J. Hunter’s 75th Birthday was orga-nized and chaired by Peter G. Taylor (Melbourne, Australia), with additionalspeakers: Stephen Kirkland (Winnipeg, Manitoba, Canada), Tugrul Dayar(Ankara, Turkey), and Guy Latouche (Brussels, Belgium). Jeff himself gavea presentation entitled “A fifty-year journey with colleagues, generalized ma-trix inverses and applied probability”.
One day after the Workshop, George and Simo (accompanied by Evelynand Soile), were relaxing in Design Centre Nini Andrade Silva Restaurantin Funchal and enjoying the harbour view. While admiring the fabulousfamily-friendly cruise ship Britannia of P & O Cruises leave the harbourmajestically, we were told by a couple of ship-spotters that one of the pas-sengers on the ship was Stephen Hawking. How about that! He had beenin Funchal on a previous day when we were completing our Workshop. Wewish he could have attended our Workshop!
Hans Joachim Werner organized a Memorial Session for Ingram Olkin(1922–2016), with additional speakers: Jeffrey J. Hunter, Simo Puntanen,and George P. H. Styan. The Session ended with an interesting and touchingvideo by Michael Greenacre (Barcelona, Spain).
The Madeira Magic Minisymposium on “Magic Squares, Prime Numbersand Postage Stamps” (organized by Ka Lok Chu & George P. H. Styan) washeld in Blandy’s Wine Lodge, Avenida Arriaga 28, in Funchal, 6 June 2016,and featured:
(1) Se-tenant philatelic Machin-definitive blocks with selected total face-values, with special emphasis on the Royal Mail “Stamps for Cooks”Prestige Booklet by Nathan Hin Shun Chu, Ka Lok Chu & GeorgeP. H. Styan.
IWMS-2016 MADEIRA REPORT: March 29, 2017 3
(2) Some comments on two sensational pandiagonal magic squares andon two philatelic magic-carpet dinner-placemats,by George P. H. Styan, Walter Trump, & Ka Lok Chu.
(3) Some comments on Sophie Germain prime numbers, by George P. H.Styan, & Ka Lok Chu.
(4) Some comments on Margaret Kepner’s 2010 “Magic Square 25 Study”by Reijo Sund, Ka Lok Chu & George P. H. Styan.
A welcome drink was part of the program. (And believe or not, accordingto George, this will be his standard for his forthcoming talks!)
Several other Invited Special Sessions and Minisymposia were arranged asfollows:
• Estimation and Testing in Linear Models (organized by Roman Zmyślony),• Methods for Modelling Correlated and Complex Data (organized byJianxin Pan),
• Multivariate Linear Models (organized by Katarzyna Filipiak),• Probability and Matrix Inequalities (organized by Alexander Ko-vačec).
The IWMS-2026 Book of Abstracts, edited by Daniel Klein & FranciscoCarvalho, includes not only the abstracts of the talks and program, but also
• “Ingram Olkin (1924–2016)—Some personal memories” by Simo Pun-tanen & George P. H. Styan: online pdf.
• “Many happy returns, Jeffrey Joseph Hunter! Personal Glimpses foryour 75th Birthday” by Simo Puntanen: online pdf.
The final program is online on the IWMS-2016 website. Selected refereedpapers presented in the Workshop will be published in an eBook Proceedingsto be published by Springer.
For previous IWMS-workshops, see our IWMS-website, from where, forexample, “A short history of the International Workshop on Matrices andStatistics” can be downloaded: online pdf. The 26th International Workshopon Matrices and Statistics will be held in 2018, the venue to be announced.
Acknowledgements. As the original version of this report was going topress, we learnt that Professor T. W. “Ted” Anderson of Stanford Univer-sity passed away on 17 September 2016. The IWMS-1998 and IWMS-2008celebrated his 80th and 90th birthdays in Fort Lauderdale (Florida, USA)and Tomar (Portugal), respectively. On his 98th birthday on 5 June 2016we sent Ted congratulations just before the IWMS-2016 Workshop. He im-mediately replied and asked us to convey his greetings to the participants.He reminded us that he had spent a 9-months sabbatical leave in Madeirain the 1960s, working on his book The Statistical Analysis of Time Series(Wiley 1971).
IWMS-2016 MADEIRA REPORT: March 29, 2017 4
As Kathleen J. Sullivan noted in her Stanford News obituary online pdf,“Amazingly, Ted submitted his last technical paper less than a month ago,”said Emmanuel Candès, chair of the Department of Statistics at Stanford,who said Anderson has been a towering intellectual figure in the departmentfor nearly 50 years.
On 10 October 2016, The New York Times published an obituary about T.W. Anderson, see the online version with the headline Theodore Anderson,Mathematician Who Advanced Data Analysis, Dies at 98. A version of thisobituary appeared in print on 11 October 2016, on page B12 of the NewYork edition with the headline: Theodore W. Anderson, 98, an EconometricsPioneer.
A modified version of this report was published in Image (The Bulletin ofthe International Linear Algebra Society), Issue Number 57, pp.18–19.
Photographs: (1) Hazel & Jeffrey J. Hunter, (2) Britannia, (3) Groupphoto in Madeira.
IWMS-2016 MADEIRA REPORT: March 29, 2017 5
