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Conference Constance van Eeden :
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Mathematical Statistics 2002
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May 24 and 25 2002
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Centre
de recherches mathématiques
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Université
de Montréal
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To
celebrate the 75th birthday of Ms Constance van Eeden,
Professor Emeritus of Université de Montréal and Honorary Professor
of the University of British Columbia, as well as her long career as a distinguished
researcher and student supervisor, the Centre de recherches mathématiques
(CRM) is proud to organize this conference. The invited speakers are Roelof
Helmers (CWI, Amsterdam), Chris A. J. Klaassen (University of Amsterdam), Denis
Larocque (HEC), Louis-Paul Rivest (Université Laval), Bill Strawderman
(Rutgers University) and Jim Zidek (UBC). Also, Yves Lepage and François Perron
of Université de Montréal will present surveys of her vast contributions
to statistical research and the advance of statistics in Québec and Canada.
Conference : Registration is free, but all
participants, including students, are urged to registrate in advance to facilitate
planning.
Banquet : A banquet will be held May 4 at 7:00PM
at Chez Queux. Tickets (40$) MUST be purchased via our web site BEFORE
MAY 15, 2002. Menu.
Schedule :
Friday May 24, 2002
9:00 - 9:15 Welcome
9:15 - 10:15 Louis-Paul Rivest, Université Laval
A directional model for the detection and treatment of crosstalk in gait
analysis
10:15 -
11:00 Coffee Break
11:00 -
12:00 Roelof Helmers, CWI Amsterdam
Statistical estimation of Poisson intensity functions
12:00 - 1:45 Lunch
1:45 - 2:15 Yves Lepage, Université
de Montréal
Nonparametric statistics: A review of Constance van Eeden's contributions
2:15 - 3:15 Denis Larocque, HEC
A review of modern methods based on signs and ranks for multidimensional
data
3:15
- 4:00 Coffee Break
4:00
- 5:00 William E. Strawderman, Rutgers University
Bayes minimax estimation of a normal mean
vector for general quadratic loss
Evening: Banquet
Saturday May 25, 2002
9:30 -
10:30 Chris A. J. Klaassen, University of Amsterdam
Asymptotically most accurate confidence intervals in the semiparametric
symmetric location model
10:30 - 11:00 François Perron,
Université de Montréal
Inference on restricted parameter spaces: A review of Constance van Eeden's
contributions
11:00
- 11:30 Coffee Break
11:30
- 12:30 Jim Zidek, UBC
Uncertainty
Abstracts :
Helmers
Statistical
estimation of Poisson intensity functions
We construct
and investigate a consistent kernel-type estimator of the intensity function of
a cyclic Poisson point process, when the period is unknown. It is assumed that
only a single realization of a Poisson process is observed in a bounded window.
In particular we prove that the estimator is consistent when the size of the
window expands. We also compute its asymptotic bias, variance and mean square
error. A simple nonparametric estimator of the period is proposed and its rate
of convergence is studied.
R.Helmers
and R.Zitikis (1999). On estimation of Poisson intensity functions, Ann. Inst.
Statist. Math., 51, 265-280.
R.Helmers,
I W.Mangku and R.Zitikis (2001). Consistent estimation of the intensity
function of a cyclic Poisson process, to appear in Journal of Multivariate
Analysis.
R.Helmers,
I W.Mangku and R.Zitikis (2001). Statistical properties of a kernel type
estimator of the intensity function of a cyclic Poisson process, CWI report
PNA-R0102, submitted for publication.
R.Helmers,
I W.Mangku (2002). On estimating the period of a cyclic Poisson process, paper
to be submitted for book in honour of Constance van Eeden.
Klaassen
Asymptotically
most accurate confidence intervals in the semiparametric symmetric location
model
One-
and two-sided confidence intervals are considered for the location parameter in
the semiparametric symmetric location model. Asymptotic bounds are proved and
confidence intervals are constructed that attain these bounds locally
asymptotically uniformly. Global uniformity is studied as well.
Larocque
A review of modern methods based on signs and ranks for
multidimensional data
In this talk, I will present some recent
developments in rank and sign based methods for multidimensional data. One of
the first attempt to generalise the well-know univariate nonparametric methods
like the sign and the Wilcoxon tests was through a componentwise approach.
Modern approaches include the spatial (or L1) method, methods based on Oja's
measure of scatter, methods based on various notions of depth, projection-based
methods and transformation-retransformation methods. I will describe these
approaches and talk about their strengths and weaknesses.
Lepage
Nonparametric statistics: A review of Constance van Eeden's
contributions
In this presentation,
we will briefly survey the important contributions of Constance van Eeden to
nonparametric statistics. We will also
evoke her exceptional involvement to building statistics in Québec and
particularly at the Université de Montréal starting in the late
sixties, as well as to the training of numerous
statisticians, notably in nonparametric statistics.
Perron
Inference on restricted parameter spaces: A review of Constance
van Eeden's contributions
In 1979, Alec Charras, a former
student of Constance van Eeden, wrote a superb Ph. D. thesis. The thesis is about the estimation of a parameter
lying in a convex set. It contains fundamental
results on the links between admissibility, Bayes estimators and extended Bayes
estimators and has led to several joint publications with Constance van Eeden.
For instance, under some regularity conditions, they show that an estimator
taking values on the boundary of the parameter space can be improved. Furthermore, they also implicitly and explicitly
provide better estimators than the usual mle in some contexts.
In particular, location families are studied.
In this talk, we shall
present some of Constance van Eeden's techniques and results. We shall also make some comments on one
particular conjecture.
Rivest
A directional model for the detection and treatment of
crosstalk in gait analysis
A
sequence {Ri : i=1,...,n} of 3x3 rotations is said
to obey the fixed axis model if, up to experimental errors, the rotation axes
of all Ri is the same, with a proper change
of the orientations of the two systems of axis used when recording the Ri's. The
fixed axis model postulates that there exist 3x3 rotation matrices A1 and A2 such
that the rotations A1'm(Ri)A2 share, for i=1,...,n, a common
rotation axis where m(Ri) represents the modal value of Ri.
Experimental errors are introduced in the model by assuming that the Ri's
follow matrix Fisher-von Mises distributions centered at m(Ri).
To fit this model, the rotations Ri are converted into 4x1 unit quaternions
qi. The fixed axis model is shown to
fit well if, up to experimental errors, the quaternions qi
lie in a two dimensional great circle on the surface of the unit sphere of R4.
Maximum likelihood estimators of the parameters are derived in terms if the eigenvectors
of the spectral decomposition of the quaternion cross-product matrix. This model
is used on data on knee movement in gait analysis. Most of this movement is flexion
about the knee flexion axis. The fixed axis model can be used to detect and correct
crosstalk, which occurs when the knee flexion axis has not been specified properly
in the experimental set-up to record the data. When crosstalk occurs, some of
the flexion movement is misinterpreted as either abduction-adduction or internal
external rotation.
Strawderman
Bayes minimax estimation of a normal mean vector for
general quadratic loss
We
consider estimation of the mean vector of a multivariate normal distribution
with arbitrary known covariance matrix and arbitrary quadratic loss function.
We attempt to unify and extend many of the known Bayes minimax results in the
literature. In particular, for any of the known hierarchical prior which give a
minimax estimator in the identity covariance matrix-identity quadratic form
loss, we give a corresponding class of minimax estimators in the general case.
Zidek
Uncertainty
Uncertainty, like its complementary cousin, information, is a much used
but not very well defined concept despite its intrinsic role in statistics. (Indeed,
that latter is often described as the "science of uncertainty".)
In
this talk, I will explore some of the meanings (provided in the manuscript accompanying
this talk written with Constance van Eeden) that are ascribed to that term and
readily discover that seemingly natural questions can have answers that are
either elusive or counter-intuitive. For example, surprisingly (in answer to one of
those
questions), the level of uncertainty (according to
one definition) can actually increase rather than decrease as the amount of
information increases. For other definitions we have not been able to give general
answers to that question.
I
will also address the issue of combining information to reduce uncertainty. Specifically, I will survey some recent work
I have done with Constance van Eeden on the use of the weighted likelihood
in conjunction with samples from populations different from, but similar
to that under study. That resemblance
can lead to very effective trade-offs of bias for precision when it derives from structural relations among the various
population parameters, for example, when the difference
in the population means may be bounded by a fixed constant.