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CONFIRMED
Akbar Azam
Random operator equations in probabilistic functional
analysis.
Philip V. Bertand
A matrix method for solving missing data problems
Nino Demetrashvili
Confidence intervals for intraclass correlation coefficients
in nonlinear mixed effects models
Sami Helle
Distance Optimal Designs for Linear Models
Xiaomi Hu
Order restricted multivariate twosample problems
Sayantee Jana
Parameter estimation and moderated trace test for the
growth curve model for highdimensional longitudinal data
Eero Liski
Averaging orthogonal projectors
Erkki P. Liski
On subspace distance and the mean of subspaces
Augustyn Markiewicz
Optimal neighbor designs under several interference
models
Mika Mattila
Estimating the eigenvalues of meet and join matrices
Joseph Nzabanita
Multivariate linear models with Kronecker product and
linear structures on the covariance matrices
Haruhiko Ogasawara
Bias adjustment minimizing the asymptotic mean square
error
Yuichiro Ogawa
A cutoff point for diagonal discriminant analysis in
high dimension
Simo Puntanen
Formulas Useful for Linear Regression Analysis and Related
Matrix Theory
Simo Puntanen
Flashes from the Second Tampere Conference
in Statistics in 1987 and the first IWMS in 1990
David TitleyPeloquin
Stochastic conditioning of systems of equations
Julia Volaufova
Twostage approximate testing in nonlinear mixed models
Hans Joachim Werner
In the Year of Statistics: C. R. Rao's IPM Method  Revisited
and Extended

AWAITING CONFIRMATION
Haftom T. Abebe,
Bayesian design for dichotomous repeated measurements
with serial correlation
Dila Ram Bhandari
Statistical Foresting: Analytical Tools
Anis Iranmanesh
Generalized Matrix T Distribution Through Generalized
Multivariate Gamma Dristribution
Zohreh
Javanshiri
Finding the information matrix for expuniform
distribution base on complete and typeII censored
data
Syeda
Rabab Mudakkar
Mudakkar Rademacher inequalities for Operators
Sathish
Pichika
Integration of miRNA and mRNA Expressions:
An Application of Sparse Canonical Correlation
Analysis (SCCA)
WITHDRAWN
Arezou Habibi Rad
Inference based on unified hybrid censored
data for Weibull distribution

Haftom T. Abebe, University
of maastricht Netherlands
Bayesian design for dichotomous repeated measurements with
serial correlation
Coauthors: Frans E. S. Tan, Gerard J. P. Van Breukelen and Martijn
P. F. Berger
In medicine and health sciences a binary outcome is often measured
repeatedly to study its change over time. A wellknown problem
for such studies is that designs that have an optimal efficiency
for some parameter values may not be efficient at all for other
parameter values. We propose Bayesian designs which formally
account for the uncertainty in the parameter values for a mixed
logistic model which allows linear or quadratic changes. The
Bayesian Doptimal allocations of time points of measurement
are computed for different priors, covariance structures and
different values of autocorrelation. Since the costs per subject
may be quite different from the costs per measurement, a subjecttomeasurement
cost ratio is taken into account when designs are compared.
The results show that the optimal number of time points increases
with the cost ratio, and that neither the optimal number nor
the optimal allocation of time points appears to depend strongly
on the prior, covariance structure, or on the amount of autocorrelation.
It also appears that for cost ratio up to five, four equidistant
time points and for larger cost ratios six equidistant time
points are highly efficient. Moreover, it seems to be more crucial
to choose the number of time points rather than to allocate
the time points as close as possible to the Bayesian optimal
design. Our results are compared with the actual design of a
study of respiratory infection in Indonesian preschool children
and with the design of a smoking prevention study in primary
school in the Netherlands.
Akbar Azam, COMSATS Institute of Information
Technology
Random operator equations in probabilistic functional analysis
Random operator theory is needed for the study of various classes
of random operator equations in probabilistic functional analysis.
During the last three decades several results regarding random
fixed points of various types of random operators have been
established and a number of their applications have been obtained
in Mathematical Statistics. In fact, random fixed point theorems
are stochastic generalizations of deterministic/classical fixed
point theorems and have important applications in random operator
equations, random differential equations and differential inclusions
.In the present talk we derive common random fixed point theorems
for multivalued random operators satisfying a contractive condition.
Philip V. Bertrand
A matrix method for solving missing data problems
Given a large data set with numbers missing at random the fitting
of multivariate distributions to it is difficult. It is shown
to be possible to fit an appropriately specified multivariate
distribution with parameters unknown using rather complex matrix
methods. Examples for the multivariate normal distribution and
for the Cox proportional hazards model are described.
Dila Ram Bhandari, Tribhuvan University
Statistical Foresting: Analytical Tools
Statistics plays a vital role in every fields of human activity.
The statistical tools like Index number, correlation, time series
analysis, regression analysis, hypothesis testing, and multivariate
analysis help to analysis data and predict about future. Forecasting
is the process of making statements about events whose actual
outcomes have not yet been observed. Statistical forecasting
concentrates on using the past to predict the future by identifying
trends, patterns and business and economic drive within the
data to develop a forecast with tools as regression analysis,
timeseries analysis and many more. Estimating the likelihood
of an event taking place in the future, based on available data.
Statistics is a set of techniques that are used in collecting,
analyzing, presenting, and interpreting data. Statistical methods
are used in a wide variety of occupations and help people identify,
study, and solve many complex problems. Statistics is also widely
used in the business and economic world. This forecast is referred
to as a statistical forecast because it uses mathematical formulas
to identify the patterns and trends while testing the results
for mathematical reasonableness and confidence. In many Forecasting
Processes, statistical forecasting forms the baseline that is
adjusted throughout the process. Risk and uncertainty are central
to forecasting and prediction; it is generally considered good
practice to indicate the degree of uncertainty attaching to
forecasts.
Nino Demetrashvili, University
of Groningen
Confidence intervals for intraclass correlation coefficients
in nonlinear mixed effects models
Coauthors: Prof. Edwin van den Heuvel
In our previous work we proposed two generic approaches for
constructing confidence intervals on intraclass correlation
coefficients (ICCs) for variance components models. The first
approach uses Satterthwhaite’s approximation and the Fdistribution.
The second approach uses the first and second moments of the
ICC estimate in combination with a Beta distribution. The variance
components were etimated with restricted maximum likelihood.
The coverage probability of the confidence intervals demonstrated
accurate results for the Betaapproach on two balanced threeway
variance components models, in particular for settings with
small sample sizes.
In our previous work we focused on linear models, but here we
investigate the performance of the Betaapproach for confidence
intervals of the ICCs in nonlinear mixed effects models. The
case study is a metaanalysis on antipsychotic medications
using MichaelisMenten curves for doseresponse relationships.
In nonlinear mixed models, restricted maximum likelihood estimation
is not well defined and different approaches are present for
variance components estimation. We present the results of a
simulation study that would compare different estimation methods.
The main focus is on small sample settings, which were driven
by our case study.
Sami Helle, Tampere University of
Technology and University of Tampere
Distance Optimal Designs for Linear Models
Coauthors: Erkki Liski (University of Tampere)
Properties of the most familiar optimality criteria, for example
A, D and Eoptimality, are well known, but the distance stochastic
optimality criterion has not drawn as much attention to date.
There exists an extensive literature on the characterization
of optimal designs under both discrete and continuous settings
using the most familiar optimality criteria. For references
see Pukelsheim (1993) and Liski et al. (2002), for example.
Though the distance stochastic criterion (DScriterion) was
put forward over forty years ago in Sinha (1970), it has attracted
attention only about ten years ago (see, for example, Liski
et al.1999, 2001; Zaigraev 2002, 2003, 2006).
In this paper we investigate properties of the DSoptimal designs
for the linear model under normally distributed errors. The
particular attention is paid to the mixture model.
References:
Liski, E. P., Mandal, N. K., Shah, K. R. and Sinha, B. K (2002),
Topics in Optimal Design, Springer,New York.
Liski, E. P. and A. Luoma and Zaigraev, A. (1999), Distance
optimality design criterion in linear models, Metrika, 49, 193211.
Liski, E. P. and Zaigraev A. (2001), A stochastic characterization
of Loewner optimality design criterion in inear models, Metrika,
53, 207222.
Pukelsheim, F. (1993), Optimal Design of Experiments, Wiley,
New York.
Sinha B. K. (1970), On the optimality of some design, Calcutta
Statistical Association Bulletin, 20, 120.
Zaigraev, A (2002), Shape optimal design criterion in linear
models, Metrika, 56, 259273.
Zaigraev (2003), Integral stochastic optimal design criteria
in linear models, Metrika, 57, 287301.
Zaigraev, A. (2006), On DSoptimal design matrices with restrictions
on rows or columns, Metrika, 64, 181189.
Xiaomi Hu, Wichita State University
Order restricted multivariate twosample problems
A p by 2 matrix is order restricted if its two columns are
linked by an order, a reflexive and transitive relation of vectors.
The projection onto the collection of all such restricted matrices
plays a vital role in order restricted multivariate twosample
estimation and testing. In this talk we define a general vector
order relation, establish the projection formula, and explore
its applications in Statistics.
Anis Iranmanesh, Islamic Azad
University
Generalized Matrix T Distribution Through Generalized Multivariate
Gamma Dristribution
Coauthors: Mohammad Arashi (Department of Mathematics, Shahrood
University of Technology, Shahrood, Iran)
In this paper, by conditioning the covariance structure of
matrix variate normal distribution the construction of a generalized
matrix ttype family is considered, thus providing a new perspective
of this family. In this regard, a generalized multivariate gamma
distribution including zonal polynomials is introduced. Some
important statistical characteristics are given. An attempt
is made to reconsider Bayes analysis of the column covariance
matrix of the underlying population model. Thus an application
of the proposed result is given in the Bayesian context of the
multivariate linear regression models.
Sayantee Jana, McMaster University
Parameter estimation and moderated trace test for the growth
curve model for highdimensional longitudinal data
Coauthors: Narayanaswamy Balakrishnan (McMaster University) Dietrich
von Rosen (Swedish university of agricultural sciences) Jemila
S Hamid (McMaster University)
Growth curve models (GCM) are an essential tool for application
in longitudinal data. The traditional tests in Growth Curve
Models collapse in highdimensional setup (n<p). So in this
study a moderated test has been proposed for testing GCM in
highdimensional scenarios. Two types of moderations were considered:
the MoorePenrose generalized inverse and Empirical Bayes’
estimator. Extensive simulations demonstrated the performance
of the moderated test, and the results were compared with the
original trace test. Distance measures were used for comparison
purposes because the parameters are matrices. Moderated MLE
and BLUE are provided for the parameter matrix and the variancecovariance
matrix and their performances were assessed using bias and MSE
which were compared to the bias and MSE of the existing MLEs
in the nonhigh dimensional setup. The approach was illustrated
using timecourse microarray data from a Lung Cancer study.
Zohreh Javanshiri
Finding the information matrix for expuniform distribution
base on complete and typeII censored data
Coauthors: Arezu Habibi Rad
The Fisher information matrix summarizes the amount of information
in the data relative to the quantities of interest. It has applications
in finding the variance of estimators, as well as in the asymptotic
behaviour of maximum likelihood estimator. In this paper, a
new distribution called the expuniform distribution is proposed.
The regularity conditions don't hold for the expuniform distribution
so we obtain the information matrix according to shao [2003],
for complete and typeII censored data.We also provide the estimator
of parameters using the maximum likelihood method. For illustrative
purpose, real data set is analysed.
Eero Liski, University of Tampere
Averaging orthogonal projectors
Coauthors: Klaus Nordhausen (University of Tampere), Hannu Oja
(University of Turku) and Anne RuizGazen (Toulouse School of
Economics).
Dimension reduction (DR) plays an important role in high dimensional
data analysis. Often the interest is on regression, where the
goal is to infer about the conditional distribution of the response
y given the pvariate explanatory vector x. One then wishes
to find an orthogonal projector P in such a way that y is independent
of x given Px. Such celebrated DR methods as sliced inverse
regression (SIR) and sliced average variance estimate (SAVE)
are adequate for finding only certain types of relationships
between y and x. Hence, we combine individual DR methods via
their corresponding orthogonal projectors and strive to provide
the best qualities of each individual DR method. This approach
finds a reduced number of uncorrelated variables and circumvents
the curse of dimensionality.
Erkki P. Liski, University of Tampere
On subspace distance and the mean of subspaces
Coauthors: Eero Liski
In multivariate problems, it is customary to use dimension
reduction (DR) techniques which share the characteristic that
the original data is projected onto a lower dimensional subspace.
Principal component analysis is a typical example. For many
applications it is the subspace, not its particular representation
that is important. Different DR methods like sliced inverse
regression and projection pursuit capture different structures
in data. The choice of the distance measure between subspaces
is crucial when comparing the performance of various DR techniques.
We address the question: How to construct a subspace distance
to establish relationships between two a more subspaces with
possible different dimensions? We present properties of alternative
subspace distances and formulate the problem of finding the
mean subspace as the computation of a matrix mean. This calls
for considering an acceptable definition for a mean of positive
semidefinite matrices. In addition to DR, subspace methods provide
a useful approach to the least squares model averaging in linear
regression and to certain fields in pattern recognition, for
example.
Augustyn Markiewicz, Poznán
University of Life Sciences
Optimal neighbor designs under several interference models
The concept of neighbor designs was introduced and defined
by Rees (1967) along with giving some methods of their construction.
Henceforth many methods of construction of neighbor designs
as well as of their generalizations are available in the literature.
However there are only few results on their optimality. Therefore
the aim of the talk is to give an overview of study on this
problem. It will include some recent results on optimality of
specified neighbor designs under various linear models. The
optimality will be studied with respect to the estimation of
a given subvector of parameters.
Mika Mattila, University of Tampere
Estimating the eigenvalues of meet and join matrices
Coauthors: Pentti Haukkanen
Let (P, ≤ ) be a lattice and f be a realvalued function
on P. In addition, let S={x_{1}, ..., x_{n}}
be a subset of P which elements are distinct and arranged so
that x_{i} ≤ x_{j}⇒ i ≤ j.
The n×n matrix having f(x_{i}∧x_{j})
as its ij element is the meet matrix of the set S with
respect to f and is denoted by (S)_{f}. Similarly, the
n×n matrix having f(x_{i}∨x_{j})
as its ij element is the join matrix of the set S with
respect to f and is denoted by [S]_{f}. In case when
(P, ≤ )=(Z_{+}, ) the matrices (S)_{f}
and [S]_{f} are referred to as the GCD and LCM matrices
of the set S with respect to f.
Despite that meetrelated matrices have been studied a lot
over the years, not much is known about their eigenvalues. Most
of the existing results concern special cases such as GCD and
LCM matrices. In fact, currently there is only one paper that
considers the eigenvalues of meet and join matrices (see [2]).
In this presentation we generalize Hong's and Enoch Lee's
[1] method and derive upper bounds for the eigenvalues of certain
meet and join matrices (S)_{f} and [S]_{f}.
As examples we consider the so called power GCD, power GCUD,
reciprocal power LCM and MIN matrices.
References:
[1] S. Hong and K. S. Enoch Lee, Asymptotic behavior of eigenvalues
of reciprocal power LCM matrices, Glasg. Math. J. 50
(2008) 163174.
[2] P. Ilmonen, P. Haukkanen and J. K. Merikoski, On eigenvalues
of meet and join matrices associated with incidence functions,
Linear Algebra Appl. 429 (2008) 859874.
Syeda Rabab Mudakkar, Lahore School
of Economics
Rademacher inequalities for Operators
Coauthors: Sergey Utev
This work is motivated by optimal bounds in Rosenthal and Khintchine
type moment inequalities. We establish several comparison results
for commutative and noncommutative random variables including
random matrices and freely independent variables.
Joseph Nzabanita, National University
of Rwanda, Linköping University
Multivariate linear models with Kronecker product and linear
structures on the covariance matrices
Coauthors: Dietrich von Rosen (Swedish University of Agricultural
Sciences) Martin Singull (Linköping University)
Models based on normally distributed random matrix are studied.
For these models, the dispersion matrix has the so called Kronecker
product structure and they can be used for example to model
data with spatiotemporal relationships. Our aim is to estimate
the parameters of the model when, in addition, one covariance
matrix is assumed to be linearly structured and the mean has
a bilinear structure. On the basis of n independent observations
from a matrix normal distribution, estimating equations in a
flipflop relation are established and numerical examples are
given.
Haruhiko Ogasawara, Otaru University
of Commerce
Bias adjustment minimizing the asymptotic mean square error
A method of bias adjustment which minimizes the asymptotic
mean square error is presented for an estimator typically given
by maximum likelihood. Generally, this adjustment includes unknown
population values. However, in some examples, the adjustment
does not include population values. In the case of a logit,
a reasonable fixed known value for the adjustment is found,
which gives the asymptotic mean square error smaller than those
of the asymptotically unbiased estimator and the maximum likelihood
estimator. The weightedscore method, which yields directly
the estimator with the minimized asymptotic mean square error,
is also given.
Yuichiro Ogawa, Tokyo University of Science
A cutoff point for diagonal discriminant analysis in high
dimension
Coauthors: Takayuki Yamada (Nihon University) and Takashi
Seo (Tokyo University of Science)
We consider the discriminant analysis of two groups when the
number of observations is larger than the total sample size.
Diagonal discriminant rule (DDR) is known as a popular rule
for the highdimensional discrimination. The DDR treated is
based on Fisher's linear discriminant rule (Wrule) and the
likelihood ratio rule (Zrule). We propose a cutoff point such
that the limiting error rate takes the minimum value under the
highdimensional framework A1: $N_1,N_2,p \to \infty, N_1/p
\to c_1 \in (0,\infty), N_2/p \to c_2 \in (0,\infty),N_1/N_2
\to c \in (0,\infty)$. By Monte Carlo simulation, we confirmed
that our proposal cutoff point takes lower error rate compared
to the zero cutoff point.
Sathish Pichika, McMaster University
Integration of miRNA and mRNA Expressions: An Application of
Sparse Canonical Correlation Analysis (SCCA)
Coauthors: Joseph Beyene
Canonical Correlation Analysis (CCA) is a multivariate statistical
method that can be used to find linear relationship between
two datasets. In highdimensional data where the number of variables
in each dataset is very large and sample size relatively small,
findings will lack robustness and biological interpretation.
Modern statistical and computational approaches are emerging
to deal with this challenge and one such method is Sparse CCA
(SCCA), where some of the variables are forced to zero leaving
with a sparse set of variable to interpret. SCCA finds linear
combinations of two datasets that include only small subsets
of variables with maximal correlation. We illustrated the methods
using real genomic datasets. Furthermore, we believe that integrating
genomic data allows us to understand the fundamental biological
processes and may help in elucidating causes of complex diseases.
Simo Puntanen, University of Tampere
Formulas Useful for Linear Regression Analysis and Related
Matrix Theory
Coauthors: George P. H. Styan (McGill University)
Even though a huge amount of the formulas related to linear
models is available in the statistical literature, it is not
always so easy to catch them when needed. The purpose of this
collection is to put together a good bunch of helpful ruleswithin
a limited number of pages, however. They all exist in literature
but are pretty much scattered. The first version (technical
report) of the Formulas appeared in 1996 (54 pages) and the
fourth one in 2008. Since those days, the authors have never
left home without the Formulas.
This book is not a regular textbookthis is supporting material
for courses given in linear regression (and also in multivariate
statistical analysis); such courses are extremely common in
universities providing teaching in quantitative statistical
analysis.
Reference
Simo Puntanen, George P. H. Styan & Jarkko Isotalo (2013).
Formulas Useful for Linear Regression Analysis and Related Matrix
Theory: It's Only Formulas But We Like Them. Springer.
Simo Puntanen, University of Tampere
Flashes from the Second Tampere Conference in Statistics in
1987 and the first IWMS in 1990
Coauthors: George P. H. Styan (McGill University) Reijo Sund (National
Institute for Health and Welfare, Helsinki) Kimmo Vehkalahti (University
of Helsinki)
In this talk we show video clips from the invited talks given
in
The Second International Tampere Conference in Statistics,
14 June 1987.
The first IWMS: International Workshop on Linear Models,
Experimental Designs, and Related Matrix Theory, Tampere, 68
August 1990.
Programs etc of these events can be downloaded from
http://people.uta.fi/~simo.puntanen/Program1987conferenceTampere.pdf
http://people.uta.fi/~simo.puntanen/Proceedings87frontmatter.pdf
http://people.uta.fi/~simo.puntanen/TampereConference87poster.jpg
http://www.sis.uta.fi/tilasto/iwms/programIWMS1990Tampere.pdf
With the assistance of Jarmo Niemela, our aim is to to provide
free access to the recorded talks by October 2013.
David TitleyPeloquin, CERFACS
Stochastic conditioning of systems of equations
Coauthors: Serge Gratton (CERFACS and ENSEEIHT, Toulouse, France)
Given nonsingular A ∈ R^{n×n} and
b ∈ R^{n}, how sensitive is x=A^{1}b
to perturbations in the data? This is a fundamental and wellstudied
question in numerical linear algebra. Bounds on ∥A^{1}b(A+E)^{1}b∥
can be stated using the condition number of the mapping (A,
b)→ A^{1}b, provided ∥A^{1}E∥
< 1. If ∥A^{1}E∥ ≥ 1 nothing can
be said, as A+E might be singular. These wellknown results
answer the question: how sensitive is x to perturbations in
the worst case? However, they say nothing of the typical
or average case sensitivity.
We consider the sensitivity of x to random noise E. Specifically,
we are interested in properties of the random variable
m(A,
b, E) = ∥ A^{1}b  (A+E)^{1}b
∥ = ∥(A+E)^{1}E x ∥, 

where vec(E) ~ (0, S)
follows various distributions. We attempt to quantify the following:
Julia Volaufova, LSUHSC School
of Public Health
Twostage approximate testing in nonlinear mixed models
Coauthors: Jeff Burton, Pennington Biomedical Research Center,
LSU, Baton Rouge, USA
We investigate here approximate small sample Ftests about
fixed effects parameters in nonlinear mixed models via two possible
approaches to estimation of population parameters. One is based
on approximating the marginal likelihood using Gaussian quadrature.
The Waldtype test statistic in this case uses the estimation
covariance matrix based on the approximate Fisher information
matrix. The adjustment coefficient and denominator degrees of
freedom depend on the total sample size and the number of population
fixedeffects parameters.
The second is the twostage approach for the case when the
number of observations per sampling unit is large enough. The
approximate Ftest is developed based on a normal approximation
to the distribution of nonlinear least squares estimates of
subjectspecific individual parameters, which constitute the
response for the second stage. The secondstage model results
in a mixed model with covariance matrix dependent on the unknown
variance components as well as on the fixed effects population
parameters. We consider this twostage approach and suggest
the use of an approximate Ftest based on approximate maximum
likelihood estimates of all model parameters. Here we focus
on comparing the performance of approximate tests under the
null hypothesis, especially accuracy of pvalues, via simulation
studies conducted for two types of pharmacokinetic models.
Hans Joachim Werner, University of
Bonn
In the Year of Statistics: C. R. Rao's IPM Method  Revisited
and Extended
In the framework of the general (possibly singular) linear
statistical model, we particularly discuss an extended IPMtype
method which is a unified method not only for obtaining estimations
but also for obtaining predictions and estimated prediction
error dispersions.
ABSTRACT WITHDRAWN
Arezou Habibi Rad, Ferdowsi
University of Mashhad
Inference based on unified hybrid censored data for
Weibull distribution
Coauthors: Fatemeh Yousefzadeh (Department of Statistics,
Birjand University)
Unified hybrid censoring is a mixture
of generalized TypeI and TypeII hybrid censoring
schemes. This article presents the statistical inferences
on Weibull parameters when the data are unified hybrid
censored. It is observed that the maximum likelihood
estimators can not be obtained in closed form. We
propose to use the numerical solution and EM algorithm
to compute the maximum likelihood estimators. We obtain
the observed Fisher information matrix using the missing
information principle and it can be used for constructing
the asymptotic confidence intervals. We also obtain
the Bayes estimates of the unknown parameters under
the assumption of independence using the Gibbs sampling
procedure. Simulations are performed to compare the
performances of the different methods and for illustrative
purposes we have analyzed one data set.
Keywords: Bayes estimators; EM algorithm;
Fisher information matrix; Gibbs sampling; Maximum
likelihood estimators; Unified hybrid censoring.
