Study on Robustness of Correlated Frailty Model
Dimitar Atanasov datanasov@fmi.unisofia.bg
AMS 2000 Subject Classification: 62J12
Key words: frailty models, robust maximum likelihood estimation.
This study considers a robust properties of correlated frailty models.
The dependence between related individuals must be considered in order to
be studied the difference between the gene information and the environment
as causes of death. To do that, one can introduce the frailty parameter
Z, which can be decomposed as Z
=Z_{g}+Z_{e}, where Z_{g} represents
the frailty, due to the gene information, and Z_{e}
represents the influence of the environment. Using the WLTE(k)
one can obtain a robust maximum likelihood estimation of the unknown
parameters of the model.
Characterization of Schrödinger Processes with Unbounded Potentials
A. Benchettah abenchettah@hotmail.com
AMS 2000 Subject Classification: 49L20, 60J60, 93E20
Key words: Schrödinger process, minimum entropy distance, stochastic optimal control, Schrödinger's system, variational
characterisation.
This work is concerned with a class of Schrödinger process with
unbounded potentials : a variant of Jamison's theorem is given without the
assumption of continuity and of everywhere strict positivity of
q. It associates with Jamison's data (q, P_{a},
P_{b}), the Csiszar's projection Q^{*}
of a reference measure R^{*} on a set
E(P_{a}, P_{b}) of probability measures with
marginals P_{a}, P_{b}. Existence of a solution
to the corresponding Schrödinger's system, construction of the
Schrödinger's bridge and variational characterisation of Schrödinger
process are established.
Assessment of Information Asymmetry
D. Christozov dgc@aubg.bg
P. Mateev pmat@math.bas.bg
AMS 2000 Subject Classification: 62P20, 91B42.
Key words: information asymmetry, warranty.
In the process of trading, the seller and buyer participate with
different initial knowledge about the technical capabilities and
about the expected use of the good. This twoside asymmetry affects
the success of the negotiation in e trading. This paper
discusses one practical approach to assess information asymmetry and
the role of warranty in sellerbuyer communication relationship. The
presented approach is illustrated with a survey experiment.
Topic Segmentation: How Much Can We Do by Counting Words and Sequences of Words
G. Dias ddg@di.ubi.pt
E. Alves elsalves@zmail.pt
C. Nunes celia@mat.ubi.pt
In this paper, we present an innovative topic segmentation system
based on a new informative similarity measure that takes into
account word cooccurrence in order to avoid the accessibility to
existing linguistic resources such as electronic dictionaries or
lexico semantic databases such as thesauri or ontology. Topic
segmentation is the task of breaking documents into topically
coherent multiparagraph subparts. Topic segmentation has
extensively been used in information retrieval and text
summarization. In particular, our architecture proposes a
languageindependent topic segmentation system that solves three
main problems evidenced by previous research: systems based uniquely
on lexical repetition that show reliability problems, systems based
on lexical cohesion using existing linguistic resources that are
usually available only for dominating languages and as a consequence
do not apply to less favored languages and finally systems that need
previously existing harvesting training data. For that purpose, we
only use statistics on words and sequences of words based on a set
of texts. This solution provides a flexible solution that may narrow
the gap between dominating languages and less favored languages thus
allowing equivalent access to
information.
Analysing Conjoint Analysis Data by a Random Coefficient Regression Model
Roberto Furlan roberto.furlan@libero.it
Roberto Corradetti roberto.corradetti@unito.it
AMS 2000 Subject Classification: 62J12, 62K15, 91B42, 62H99.
Key words: conjoint analysis, random coefficient regression model, full factorial design, fractional
factorial design, design matrix
Since late 1960s conjoint analysis has been applied in estimating consumer preferences in marketing research.
A Note on the Extinction Problem for Controlled Multitype Branching Processes
Miguel González mvelasco@unex.es
Rodrigo Martínez rmartinez@unex.es
Manuel Mota mota@unex.es
AMS 2000 Subject Classification: 60J80, 60J10.
Key words: controlled multitype branching processes, random control, homogeneous mutitype Markov chains.
In this paper we consider a discrete time controlled multitype
branching process with random control in discrete time. We provide
sufficient conditions for the almost sure extinction of the process
as well as for its indefinite growth with a positive probability.
Moreover an illustrative example is shown and some simulations are
given.
Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast
Cancer Treatment
Dario Gregori
Rosalba Rosato
Giovannino Ciccone
Lara Lusa
In nonlinear random effects some attention has been very
recently devoted to the analysis ofsuitable transformation of the
response variables separately (Taylor 1996) or not (Oberg and
Davidian 2000) from the transformations of the covariates and, as
far as we know, no investigation has been carried out on the choice
of link function in such models. In our study we consider the use of
a random effect model when a parameterized family of links
(ArandaOrdaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and
Czado 1997) is introduced. We point out the advantages and the
drawbacks associated with the choice of this datadriven kind of
modeling. Difficulties in the interpretation of regression
parameters, and therefore in understanding the influence of
covariates, as well as problems related to loss of efficiency of
estimates and overfitting, are discussed. A case study on
radiotherapy usage in breast cancer treatment is
discussed.
Statistical Inference for Processes Depending on Environments and Application in Regenerative
Processes
Christine Jacob cj@banian.jouy.inra.fr
Nadia Lalam
Nickolay Yanev yanev@math.bas.bg
We consider a process {Z_{n}}_{{n in
N}}, recursively defined by Z_{n} =
f(F_{n1},E_{n}) + h
_{n}, where F_{n1}={Z_{k}}_{k £ n1},
E_{{n}}={C_{k}}_{k£
n}, {C_{n}}_{n} is an observed exogenous
process and {h _{n}}_{n} is
a martingale difference sequence for the filtration generated by
(F_{n1}, E_{n}) such that Var(h
_{n}F_{n1},E_{n})g(F_{n1},E_{n})
< ¥ , a.s. for some known function
{g(F_{n1},E_{n})}_{n}. This class of models
covers a very broad range of models such as regression models, ANOVA
models, autoregressive processes, branching processes, regenerative
processes, ... We assume that f(F_{n1},E_{n})
depends on an unknown parameter m
_{0} and that by notation f(.)= f_{m0}(.) may be decomposed
according to f_{m0}(.)=f^{(1)}_{q0}(.) +
f^{(2)}_{m0}(.),
where q _{0} in R
^{d}, dz < ¥ , is asymptotically
identifiable in f^{(1)}_{q0}(.) as n ®
¥ at some rate v(.) whereas
f^{(2)}_{m0}(.)v(.) is asymptotically
negligible. We build the Conditional Least Squares Estimator of
q _{0} based on the observation of
a single trajectory of {Z_{k},C_{k}}_{k},
and give conditions ensuring its strong consistency. The particular
case of general linear models according to m _{0}=(q_{0},n_{0}) and among them, regenerative
processes, are studied more particularly. In this frame, we may also
prove the consistency of the estimator of n
_{0} although it belongs to an asymptotic negligible part of
the model, and the asymptotic law of the estimator may also be
calculated.
Sensitivity Analysis of the Risk of Forecasting for Autoregressive Time Series with Missing Values
Yu. S. Kharin kharin@bsu.by
A. S. Huryn hurynaliaksandr@yahoo.com
AMS 2000 Subject Classification: 62M20, 62M10, 6207.
Key words: forecasting, autoregression, missing values, risk, sensitivity
The problems of statistical forecasting of vector autoregressive
time series with missing values are considered for different levels
of prior information on the parameters of the underlying model. The
mean square risk of forecasting and the risk sensitivity coefficient
are evaluated and analyzed. Results of numerical experiments are
presented.
Comparison between Numerical and Simulation Methods for Agedependent Branching Models with Immigration
R. Martínez rmartinez@unex.es
M. SlavtchovaBojkova bojkova@math.bas.bg
AMS 2000 Subject Classification: 60J80, 60J85
Key words: agedependent branching processes with immigration at zero state, numerical computations, MonteCarlo
method
This work aims to provide and to compare numerical computation
and simulation method to estimate the distribution of some relevant
variables related to an agedependent model allowing immigration at
state zero. Specifically, we analyze the behaviour of the following
variables: the extinction time and the waiting time for the
beginning of the survival of population forever. They are strongly
related to the population and repopulation experiments in biology
and to the wastewater treatment, as well. Throughout the paper, we
illustrate the methods provided by some proper examples.
Nonparametric Estimation in the Class of Bisexual Processes with PopulationSize Dependent Mating
Manuel Molina mmolina@unex.es
Manuel Mota mota@unex.es
Alfonso Ramos aramos@unex.es
AMS 2000 Subject Classification: 60J80, 62M05
Key words: bisexual branching processes,
populationsize dependent processes, nonparametric inference,
asymptotic properties.
In this paper the class of bisexual branching processes with
populationsize dependent mating is considered. Nonparametric
estimators and confidence intervals for the main parameters involved
in such a class of stochastic models are provided. For the proposed
estimators, the main conditional to nonextinction and conditional
moments are established and some asymptotic properties are
investigated. As illustration, a simulated example is given.
Some Inequalities of the Uniform Ergodicity and Strong Stability of Homogeneous Markov Chains
Zahir Mouhoubi z_mouhoubi@yahoo.fr
Djamil Aiissani
AMS 2000 Subject Classification: 60J45, 60K25
Key words: quantitative estimates, uniform ergodicity, stability, strong stability, perturbation.
In this paper we have established some uniform and strong
stability estimates for homogeneous Markov chains under mixing
conditions. As a general rule, the initial parameters values of the
most complex systems has approximately known (they are defined on
basis statistics methods), which involve errors for the calculus of
research characteristics for each studied system. For this, the
stability inequalities obtained in this paper allow us to use them
in order to estimate numerically the error of definition for
concerned characteristics, for a small perturbations of system's
parameters. As an example of application, we are interesting about
the well known waiting process where we consider the perturbation
for the characteristics of the system when we apply a small
perturbation for the control sequence.
Trimmed Likelihood Estimation of the Parameters of the Generalized Extreme Value Distributions: a MonteCarlo Study
Neyko Neykov neyko.neykov@meteo.bg
Rositsa Dimova rdimova@fmi.unisofia.bg
Plamen Neytchev plamen.neytchev@meteo.bg
AMS 2000 Subject Classification: 62F35, 62P99
Key words: generalized extreme value distribution, maximum likelihood estimation, trimmed likelihood
estimation, MonteCarlo simulation.
The applicability of the Trimmed Likelihood Estimator (TLE)
proposed by Neykov and Neytchev to the extreme value distributions
is considered. The effectiveness of the TLE in comparison with the
classical MLE in the presence of outliers in various scenarios is
illustrated by an extended simulation study. The FASTTLE algorithm
developed by Neykov Müuller is used to get the parameter estimate.
The computations are carried out in the R environment using the
packages ismev originally developed by Coles and ported in R
by Stephenson.
SplitARCH
Biljana Popović biljanap@junis.ni.ac.yu
Vladica Stojanović vlada70@verat.net
AMS 2000 Subject Classification: 62M10
Key words: conditional heteroscedasticity, conditional least squares
We supplied the GARCH Zoo with the new model and introduce it in
this paper. We named it SplitARCH. It was empirically
motivated by means of the real data set on soybean meal price on the
Product exchange. SplitARCH is the superstructure of the previously
known models of GARCH type. We defined volatility exchange to follow
sudden and great changes of the price, and volatility also. As far
as the log returns of the price are defined as X_{n}=s_{n}e_{n}, we set the volatility to be
s _{n}^{2}=a_{0} +å
^{p}_{j=1} a _{j}
X_{nj}^{2} +å
^{q}_{k=1} f_{k}(s_{nk}^{2}) I(e _{nk}^{2} >c ) n³ 0 with the threshold c>0. Under the
stationarity conditions and specified f, we discus the possibilities
of estimating parameters in this paper also.
Logistic Regression in Modelling Data for CVC  Related Infection
Krasimira Prodanova kprod@tusofia.bg
Ionko Stoinov
Dimitar Terziiski
AMS 2000 Subject Classification: 62J12, 62P10
Key words: Central Venious Catheter (CVC)infection, multinomial logistic regression
A prospective study of all new central venous catheters (CVC)
inserted for patients in intensive care unit in order to identify
risk factors for CVC infection and to determine the rate of CVC
related infection is undertaken. A catheterrelated infection and
sepsis was suspected in 62 cases of 118 CVC inserted in intensive
care patients. A multiple logistic regression to obtain adjusted
estimate of odds ratios and to identify which factors were
associated independently with CVC related infection was performed.
The variables which entered in the model were those found to be
statistically significant (\alpha &le: 0.5) on univariate
analysis and those which were established risk factors from previous
research reports. The dependent variable was the CVC related
infection. The independent variables were ten: age, sex, insertion
site, number of lumens, duration of catheterization etc. The
software package STATISTICA 6.0 was used for analyzing the real
data.
Application of Statistical Experimental Design in Food Sciences
Ute Römisch ute.roemisch@tuberlin.de
The development of new, health supporting food of high quality
and the optimization of food technological processes today require
the application of statistical methods of experimental design. The
principles and steps of statistical planning and evaluation of
experiments will be explained. By example of the development of a
glutenfree rusk (zwieback), which is enriched by roughage compounds
the application of a simplexcentroid mixture design will be shown.
The results will be illustrated by different
graphics.
Modelling Covariates in Multipath Change
N. Sanjari Farsipour nsf@susc.ac.ir
AMS 2000 Subject Classification: 62N02
Key words: covariate, maximum likelihood, modelling, multipath changepoint problems.
In the multipath change  point problems, it is often of interest
to assess the impact of covariates on the change point itself as
well as on the parameter before and after the change point. In this
paper, we consider a simple model for the changepoint distribution,
and then through hazard, we include covariates in the change point
distribution. Maximum likelihood estimation is discussed.
Probabilistic Approach to Design of Large Antenna Arrays
Blagovest Shishkov bshishkov@math.bas.bg
Hiroshi Matsumoto matsumot@rish.kyotou.ac.jp
Naoki Shinohara shino@rish.kyotou.ac.jp
AMS 2000 Subject Classification: 78A50
Key words: microwave power transmission,
large antenna array, uniform spacing, random spacing, spatial and
amplitude tapering, sidelobe level, grating lobes, workspace,
transmitting efficiency.
Recent advances in space exploration have shown a great need for
antennas with high resolution, high gain and low sidelobe (SL)
level. The last characteristic is of paramount importance especially
for the Microwave Power Transmission (MPT) in order to achieve
higher transmitting efficiency. In this concern statistical methods
play an important role. Various probabilistic properties of a large
antenna array with randomly, uniformly and combined spacing of
elements are studied and especially the relationship between the
required number of elements and their appropriate spacing from one
part and the desired SL level, the aperture dimension, the beamwidth
and transmitting efficiency from the other. We propose a new unified
approach in searching for reducing SL level by exploiting the
interaction of deterministic and stochastic workspaces of proposed
algorithms, emphasizing on the distribution of the maximums of SL
level. These models indicate any advantages with respect to
sidelobes in the large area around the main beam. A new concept of
designing a large antenna array system is proposed. Our theoretic
study and simulation results clarify how to deal with the problems
of sidelobes in designing a large antenna array, which seems to be
an important step toward the realization of future SPS/MPT
systems.
Weak Convergence to the Tangent Process of the Linear Multifractional Stable Motion
Stilian Stoev sstoev@bu.edu
Murad S. Taqqu murad@bu.edu
AMS 2000 Subject Classification: 60G18, 60E07
Key words: path continuity, Hölder regularity, linear fractional stable motion, selfsimilarity,
multifractional Brownian motion, local selfsimilarity, heavy tails.
The linear multifractional stable motion (LMSM), Y={Y(t)}_{{t
in R}}, is an astable
(0<a<2) stochastic process which
exhibits local selfsimilarity. It is constructed by using a
stochastic integral representation of the linear fractional stable
motion (LFSM) process X_{H,a}(t),
where the selfsimilarity exponent H is replaced by a function H(t)
in (0,1) of time t. Here, we focus on LMSM processes with continuous
paths and study the convergence {1/d(l)(Y(lt + t_{0})
 Y(t_{0}))}_{t in [1,1]} Þ {Z(t)}_{t in [1,1]}, as ¯0, where Þ denotes the
weak convergence of probability distributions on the space of
continuous functions C[1,1] equipped with the uniform
norm and where d(l) ¯ 0. We show that if the function H(t) is
sufficiently regular and if 1/a<H(t_{0})<1, then the above weak
convergence holds with normalization d(l)=l^{H(t0)} and the limit
(tangent) process Z(t) is the LFSM
X_{H(t0),a}(t). We also
show that one can have degenerate tangent processes Z(t), when the
function H(t) is not sufficiently regular. The LMSM process is
closely related to the Gaussian multifractional Brownian motion
(MBM) process. We establish similar weak convergence results for the
MBM.
Parametric Estimation in Branching Processes with an Increasing Random Number of Ancestors
Vessela Stoimenova stoimenova@fmi.unisofia.bg
Nickolay Yanev yanev@math.bas.bg
AMS 2000 Subject Classification: 60J80, 62M05
Key words: branching processes, random number of ancestors, power series distribution, parametric estimation,
consistency, asymptotic normality, efficiency.
The paper deals with a parametric estimation in branching
processes {Z_{t}(n)} having random number of ancestors
Z_{0}(n) as both n and t tend to infinity (and thus
Z_{0}(n) in some sense). The offspring distribution is
considered to belong to a discrete analogue of the exponential
family  the class of the power series offspring distributions.
Consistency and asymptotic normality of the estimators are obtained
for all values of the offspring mean m, 0<m<¥, in the subcritical, critical and supercritical
case.
Comparison of Multivariate and Univariate Models for Genetic Evaluation of Milk Yield based on Test Day Data
Yanka Tsvetanova yanka@unisz.bg
AMS 2000 Subject Classification: 62H12, 62P99
Key words: mixed linear models, repeated measures, fixed regression, genetic parameters
Multivariate and univariate lactation models were applied to test
day data to predict genetic value of daily milk yield of a sample of
Black and White cows. The models for genetic evaluation include a
set of fixed main effects, fixed regression on functions of days im
milk, random effects of permanent environment within lactation,
random additive genetic effect and residual effect. Under
multivariate model for daily milk yield test day records within
lactation are considered as repeated measurements, and different
lactations are treated as separate traits. Univariate model is
applied for each lactation using test day yield as repeated measure.
The variance components, genetic parameters and ranging of the
animals through the multivariate and univariate metod were
compared.
Stochastic Optimization in Robust Statistic
D. Vandev
AMS 2000 Subject Classification: 62J05, 62G35
Key words: robust estimators of location, least median of squares, stochastic approximation algotithm, MonteCarlo study.
The paper studies a stochastic optimization algorithm for
computing of robust estimators of location proposed by Vandev
(1992). A random approximation of the exact solution was proposed
which is much cheaper in time and easy to program. Two examples are
presented. Besides standard estimators of location like trimmed mean
also robust regressions (LMS and LTS) introduced by Rousseeuw and
Leroy are considered. MATLAB programs are included.
Statistical Analysis of Data on Linker Histones/DNA Interactions
J. Yaneva
N. Daskalova nina_rdm@yahoo.com
N. Yanev yanev@math.bas.bg
AMS 2000 Subject Classification: 62P10, 92C40
Key words: linker histones/DNA interactions, anticancer antibiotics, chisquare test.
Linker histones (H1, H1o H5, subtypes and variants) play a
pivotal role in formation of higher order chromatin structure and
thus  as main regulators of the expression of genetic information
kept in DNA. That is why the knowledge of the nature of linker
histones/DNA interactions is of a greatest interest in understanding
of such important issues as transcription regulation, cell division,
and cancerogenesis. As DNA is a main "target" of most anticancer
antibiotics, the analysis of competitive reactions between that
drugs (in our case actinomycin D and netropsin) and linker histones
for binding to certain sites in DNA gives hopeful information
concerning the mode of such interactions. In this work we present
statistical analysis of some experimental data concerning the
influence of some anticancer antibiotics on linker histones/DNA
interactions. First, it was investigated the formulated hypothesis
of the dependence of H1/DNA interaction on actinomycin D
concentration. Such a relation was expected knowing the different
mode for binding of the both drugs to DNA double helix. The applied
statistical analysis using chisquare test for independence showed
that the concentration of Actinomycin D in reaction mixture had no
essential effect on linker histone/DNA binding. On the contrary, the
same analysis with the second antibiotic  netropsin showed that we
could not reject the hypothesis of dependence. Some other
statistical models are also proposed, applying chisquare test for
homogeneity, test of Willcockson, Smirnov's test and others.
Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes
Kosto V. Mitov kmitov@afacad.bg
AMS 2000 Subject Classification: 60J80, 60G70
Key words: bivariate geometric distributions, bisexual branching processes, varying environments, maximum family
sizes.
We obtain a limit theorem for the row maximum of a triangular
array of bivariate geometric random vectors. An application of this
limit theorem is provided for maximum family size within a
generation of a bisexual branching process with varying geometric
offspring laws.
