Recent Advances in Linear Models and Related Areas: Essays in Honour of Helge Toutenburg

447 Pages·2008·4.055 MB·English

by  Dr. Shalabh, Dr. Christian Heumann (auth.)

Recent Advances in Linear Models and Related Areas
Shalabh Christian Heumann
●
Recent Advances in Linear
Models and Related Areas
Essays in Honour of Helge Toutenburg
Dr. Shalabh Dr. Christian Heumann
Department of Mathematics & Statistics Institute of Statistics
Indian Institute of Technology Kanpur Ludwig-Maximilians-University Munich
Kanpur - 208016 India Akademiestr. 1
[email protected] 80799 Munich
[email protected]
ISBN 978-3-7908-2063-8 e-ISBN 978-3-7908-2064-5
Library of Congress Control Number: 2008929501
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Preface
This collection contains invited papers by distinguished statisticians to
honour and acknowledge the contributions of Professor Dr. Dr. Helge
Toutenburg to Statistics on the occasion of his sixty-fifth birthday.
These papers present the most recent developments in the area of the
linear model and its related topics.
Helge Toutenburg is an established statistician and currently
a Professor in the Department of Statistics at the University of
Munich (Germany) and Guest Professor at the University of Basel
(Switzerland). He studied Mathematics in his early years at Berlin and
specialized in Statistics. Later he completed his dissertation (Dr. rer.
nat.) in 1969 on optimal prediction procedures at the University of
Berlinand completedthe post-doctoral thesisin 1989at the University
of Dortmund on the topic of mean squared error superiority. He taught
at the Universities of Berlin, Dortmund and Regensburg before joining
the University of Munich in 1991.
He has various areas of interest in which he has authored and
co-authored over 130 research articles and 17 books. He has made
pioneering contributions in several areas of statistics, including linear
inference, linear models, regression analysis, quality engineering,
Taguchi methods, analysis of variance, design of experiments, and
statistics in medicine and dentistry. His most influential contributions
are in the area of optimal prediction in linear models, mean squared
error superiority of biased estimators, weighted mixed estimation in
missing data analysis, repeated measures designs and the unification
of various parameterizations of the carry-over effect in cross-over
designs. His books Prediction and Improved Estimation in Linear
VI Preface
Models (Wiley) and Prior Information in Linear Models (Wiley) laid
the foundations for further work in the field of utilization of prior
information as well as in the field of prediction. Other pioneering
works include Linear Models and Generalizations: Least Squares and
Alternatives (Springer) and Statistical Analysis of Designed Experi-
ments (Springer). His books in German on descriptive and inductive
statistics, quality engineering, design of experiments and linear models
are among the popular textbooks in several universities in Germany.
He has also translated the celebrated books of Professor C.R. Rao
into German. His book on statistics in dentistry is the first book in
German in this area.
Helge Toutenburg maintains fruitful research collaboration with
researchers in different countries like the USA, India, Korea, etc. He
has hosted DAAD and Humboldt fellows. He is not only a well known
researcher but also an excellent teacher. He has advised Ph.D. students
from germany and abroad. His efficient working style has always been
appreciatedbythosewhohadachancetocollaboratewithhim.Hehas
been actively associated with the International Statistical Institute,
Deutscher Hochschulverband, Deutsche Statistische Gesellschaft,
Biometrical Society and Bernoulli Society for Mathematical Statistics
and Probability.
Besides having a great interest in statistics, Helge Toutenburg has
a great sense of humor, too. He has written several books on humor in
German to the pleasure of his friends and colleagues.
This collection of invited papers brings together the recent deve-
lopments in the field of linear models and its related sub-fields as well
as papers from Helge Toutenburg‘s other areas of interest.
As the editors of this book, we would like to express our heart-
ful thanks to the authors whose contributions and commitment made
this book possible. We would like to thank Michael Schomaker for his
immense help in the editorial process and Valentin Wimmer for his
help in typing. We are also thankful to Dr. Mu¨ller of Springer for his
cooperation in the publication of this book.
Munich, Shalabh
June, 2008 Christian Heumann
Contents
On the Identification of Trend and Correlation in
Temporal and Spatial Regression
Ludwig Fahrmeir, Thomas Kneib ............................ 1
Estimating the Number of Clusters in Logistic
Regression Clustering by an Information Theoretic
Criterion
Guoqi Qian, C. Radhakrishna Rao, Yuehua Wu, Qing Shao ..... 29
Quasi Score and Corrected Score Estimation in the
Polynomial Measurement Error Model
Hans Schneeweiss .......................................... 45
Estimation and Finite Sample Bias and MSE of FGLS
Estimator of Paired Data Model
Weiqiang Qian, Aman Ullah ................................ 59
Prediction of Finite Population Total in Measurement
Error Models
Hyang Mi Kim, A.K.Md. Ehsanes Saleh ...................... 79
The Vector Cross Product and 4×4 Skew-symmetric
Matrices
Go¨tz Trenkler, Dietrich Trenkler ............................. 95
Simultaneous Prediction of Actual and Average Values
of Response Variable in Replicated Measurement Error
Models
Shalabh, Chandra Mani Paudel, Narinder Kumar .............. 105
VIII Contents
Local Sensitivity in the Inequality Restricted Linear
Model
Huaizhen Qin, Alan T.K. Wan, Guohua Zou .................. 135
Boosting Correlation Based Penalization in Generalized
Linear Models
Jan Ulbricht, Gerhard Tutz.................................. 165
Simultaneous Prediction Based on Shrinkage Estimator
Anoop Chaturvedi, Suchita Kesarwani, Ram Chandra........... 181
Finite Mixtures of Generalized Linear Regression
Models
Bettina Gru¨n, Friedrich Leisch .............................. 205
Higher-order Dependence in the General Power ARCH
Process and the Role of Power Parameter
Changli He, Hans Malmsten, Timo Tera¨svirta ................. 231
Regression Calibration for Cox Regression Under
Heteroscedastic Measurement Error — Determining
Risk Factors of Cardiovascular Diseases from
Error-prone Nutritional Replication Data
Thomas Augustin, Angela Do¨ring, David Rummel.............. 253
Homoscedastic Balanced Two-fold Nested Model when
the Number of Sub-classes is Large
Shu-Min Liao, Michael Akritas .............................. 279
QR-Decomposition from the Statistical Point of View
Hilmar Drygas............................................. 293
On Penalized Least-Squares: Its Mean Squared Error
and a Quasi-Optimal Weight Ratio
Burkhard Schaffrin ......................................... 313
Optimal Central Composite Designs for Fitting Second
Order Response Surface Linear Regression Models
Sung Hyun Park, Hyuk Joo Kim, Jae-Il Cho................... 323
Does Convergence Really Matter?
Jo¨rg Drechsler, Susanne Ra¨ssler ............................. 341
Contents IX
OLS-Based Estimation of the Disturbance Variance
Under Spatial Autocorrelation
Walter Kra¨mer, Christoph Hanck ............................ 357
Application of Self-Organizing Maps to Detect
Population Stratification
Nina Wawro, Iris Pigeot .................................... 367
Optimal Designs for Microarray Experiments with
Biological and Technical Replicates
Rashi Gupta, Panu Somervuo, Sangita Kulathinal, Petri Auvinen 389
Weighted Mixed Regression Estimation Under Biased
Stochastic Restrictions
Christian Heumann, Shalabh ................................ 401
Coin Tossing and Spinning – Useful Classroom
Experiments for Teaching Statistics
Helmut Ku¨chenhoff......................................... 417
Linear Models in Credit Risk Modeling
Thomas Nittner............................................ 427
Index.................................................... 441
List of Contributors
A.K.Md. Ehsanes Saleh Bettina Gru¨n Technische
Carleton University/School of Universita¨t Wien/Institut
Mathematics and Statistics fu¨r Statistik und Wahrschein-
Ottawa, Canada lichkeitstheorie Wiedner
[email protected] Hauptstrasse 8-10 - 1040 Vienna,
Austria
Alan T.K. Wan City University [email protected].
of Hong Kong/Department of at
Management Sciences - Kowloon,
Hong Kong
Burkhard Schaffrin Ohio State
[email protected]
University/School of Earth
Sciences - Columbus Ohio, U.S.A.
Aman Ullah University of
[email protected]
California/Department of
Economics University Avenue 900
C. Radhakrishna Rao Penn
- Riverside, CA 92521, U.S.A.
State University/Department of
[email protected]
Statistics PA 16802 - University
Park, U.S.A.
Angela D¨oring GSF-National
[email protected]
Research Center for
Environment and Health,
Chandra Mani Paudel Tribhu-
Ingola¨stter Landstrasse 1, 85764
van University/Department
Neuherberg, Germany
of Statistics - Pokhra, Nepal
[email protected]
[email protected]
Anoop Chaturvedi University
of Allahabad/Department of Changli He Dalarna University
Statistics - Allahabad, India - Dalarna, Sweden
[email protected] [email protected]
XII List of Contributors
Christian Heumann University G¨otz Trenkler University of
of Munich/Department of Dortmund/Department of
Statistics Akademiestrasse 1 - Statistics Vogelpothsweg 87 -
80799 Munich, Germany 44221 Dortmund, Germany
christian.heumann@stat. trenkler@statistik.
uni-muenchen.de uni-dortmund.de
Christoph Hanck University of
Guohua Zou University of
Dortmund/Department of
Rochester/Department of
Statistics Vogelpothsweg 78 -
Biostatistics and Computational
44221 Dortmund, Germany
Biology Rochester, NY 14642,
christoph.hanck@
U.S.A.
uni-dortmund.de
Guohua [email protected].
edu
David Rummel emnos GmbH
Theresienho¨he12-80339Munich,
Germany d [email protected] Hans Malmsten
La¨nsfo¨rs¨akringar - Stockholm,
Dietrich Trenkler University of
Sweden Hans.Malmsten@
Osnabru¨ck/Rolandstrasse 8
lansforsakringar.se
- 49069 Osnabru¨ck, Germany
[email protected].
Hans Schneeweiss University
uni-osnabrueck.de
of Munich/Department of
Friedrich Leisch University of Statistics Ludwigstrasse 33 -
Munich/Department of 80539 Munich, Germany
Statistics Ludwigstrasse 33 - [email protected]
80539 Munich, Germany
Friedrich.Leisch@stat.
Helmut Ku¨chenhoff University
uni-muenchen.de
of Munich/Department of
Statistics Akademiestrasse 1 -
Guoqi Qian University of
80799 Munich, Germany
Melbourne/Department of
helmut.kuechenhoff@stat.
Mathematics and Statistics VIC
uni-muenchen.de
3010 - Melbourne, Australia
[email protected]
Hilmar Drygas University of
Gerhard Tutz University of Kassel/Department of
Munich/Department of Statistics Mathematics - 34109 Kassel,
Akademiestrasse 1 - 80799 Germany
Munich, Germany [email protected].
[email protected] kassel.de