Contributions to Probability and Statistics : Applications and Challenges - Proceedings of the International Statistics Workshop

323 Pages·2006·12.963 MB·English

by  Peter Brown, Shuangzhe Liu, Dharmendra Sharma

CONTRIBUTIONS TO
PROBABILITY AND STATISTICS
APPLICATIONS AND CHALLENGES
PETER BROWN SHUANGZHE LIU DHARMENDRASHARMA
CONTRIBUTIONS TO
PROBABILITY AND STATISTICS
APPLICATIONS AND CHALLENGES

"'*£,
Proceedings of the International
Statistics Workshop
University of Canberra
4-5 April 2005
CONTRIBUTIONS TO
PROBABILITY AND STATISTICS
APPLICATIONS AND CHALLENGES
PETER BROWN • SHUANGZHE LIU • DHARMENDRASHARMA
University of Canberra
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CONTRIBUTIONS TO PROBABILITY AND STATISTICS:
APPLICATIONS AND CHALLENGES
Proceedings of the International Statistics Workshop
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Preface
The International Statistics Workshop was held at the University of
Canberra, Canberra, Australia on 4-5 April 2005. It was timed to fit in
with the 55th Session of the International Statistical Institute (ISI) held in
Sydney, Australia, from 5 to 12 April 2005.
Attending were a number of international academics, academics from
around Canberra (Australian National University (ANU), Australian De
fense Force Academy (attached to University of New South Wales) (ADFA),
Commonwealth Scientific and Industrial Research Organisation (CSIRO)
and various Commonwealth Government Departments), academics from
within the University of Canberra with research interests in the area, and
members of the Mathematics and Statistics Discipline at the University of
Canberra.
It was a pleasure to welcome the many international and local speak
ers, participants and friends to the workshop. Speakers addressed topics
in probability and statistics, with applications, both specialised and gen
eral. All contributions were strongly research and/or application oriented.
The Workshop was arranged to include especially the areas of interest at
the University of Canberra: applications in economic and financial areas,
ecology and psychology, teaching and education, health and sports studies,
and computer and IT-data mining, in addition to statistical theory and
methodology.
We wish to thank the many contributors, referees and participants, with
out whose efforts the Workshop and these Proceedings would not have been
possible. In particular, we would like to thank Joe Gani, Chris Heyde and
George Styan for their thoughtful advice and assistance in the organisation
of the workshop and in the editing process during the last two years. We
also wish to thank Daryl Daley, Peter Hall, Mary Hewett, Ian Lisle, Mike
Osborne and Alan Welsh for their support on various matters. Finally, we
thank the staff members of the School of Information Sciences and En-
vi Preface
gineering and of the University of Canberra more widely who have been
involved in arranging and supporting the Workshop and Proceedings.
Peter Brown, Shuangzhe Liu & Dharmendra Sharma
Editors.
Organising group: Shuangzhe Liu, Dharmendra Sharma and Peter Brown;
Editorial group: Peter Brown, Shuangzhe Liu and Dharmendra Sharma;
all at
School of Information Sciences and Engineering,
University of Canberra.
CONTENTS
Preface
Part A Mathematics and Statistics in Society 1
Estimating Internet Access for Welfare Recipients in Australia 3
A. Daly & R. Lloyd
Two Classification Methods of Individuals for Educational
Data and an Application 11
A. Hayashi
Measurement of Skill and Skill Change 17
R. Kelly & P. E. T. Lewis
Some Comments about Issai Schur (1875-1941) and the Early
History of Schur Complements 28
S. Puntanen & G. P. H. Styan
Part B Applications of Statistics 67
Estimating the Number of SARS Cases in Mainland China in
2002-3 69
J. Gani
Using Statistics to Determine the Effectiveness of Prescribed Burning 73
K. J. King & J. Chapman
viii Contents
A Fair Tennis Scoring System for Doubles in the Presence of
Sun and Wind Effects - An Application of Probability 89
G. Pollard
Part C Theoretical Issues in Probability and
Statistics 97
Perturbed Markov Chains 99
J. J. Hunter
Matrix Tricks for Linear Statistical Models: A Short Review
of our Personal Top Fourteen 113
J. Isotalo, S. Puntanen & G. P. H. Styan
On Influence Diagnostics in Multivariate Regression Models
under Elliptical Distributions 129
S. Liu
A Necessary Condition for Admissibility of Nonnegative
Quadratic Estimators of Variance Components when the Mo
ments are not Necessarily as under Normality 142
C.-Y. Lu, Y. Gao & B. Zhang
Small-Sample Performance of Robust Methods in Logistic Regression 152
S. Nargis & A. Richardson
On the Asymptotic Distribution of the 'Natural' Estimator
of Cronbach's Alpha with Standardised Variates under Non-
normality, Ellipticity and Normality 167
H. Neudecker
On the Approximate Variance of a Nonlinear Function of
Random Variables 172
H. Neudecker & G. Trenkler
On Oblique and Orthogonal Projectors 178
G. Trenkler
Contents ix
Fiducial Inference of Means and Variances from Normal
Populations under Order Restrictions 192
B. X. Zhang, X. Z. Xu & X. Li
Part D Probabilistic Models in Economics and
Finance 209
When Large Claims are Extremes 211
R. Gay
Shrinkage Estimation of Gini Index 234
R. Ghori, S. E. Ahmed & A. A. Hussein
On the Problem of Discriminating between the Tails of Distributions 246
C. C. Heyde & K. Au
Part E Numerical Methods 259
An Approximate Maximum a Posteriori Method with Gaus
sian Process Priors 261
M. Hegland
Data Extraction for Improved Prediction Outcomes in Organ
Transplantation — A Hybrid Approach 276
F. Shadabi et al.
Mining Multiple Models 289
G. J. Williams
Part F Abstracts without Papers 297
Ranked Set Sampling: A Simple Idea of Great Use 299
Z. Chen
Properties of Nearest-neighbour Classifiers 300
P. Hall