﻿ Pliska Studia Mathematica Bulgarica Volume 14, 2003

### Pliska Studia Mathematica Bulgarica

Volume 14, 2003

Proceedings of the Seminar on Statistical Data Analysis, Varna, 2003

GUEST EDITOR: D. Vandev

Sofia, 2003

#### A B S T R A C T S

ABOUT THE CONCEPT OF WEIGHTS OF WLTE(K) ESTIMATORS
Dimitar Atanasov datanasov@fmi.uni-sofia.bg

1991 Mathematics Subject Classification:62F35, 62F15.
Key words: Robust statistics, WLT Estimators, Bayes Estimator.

The concept for trimming and weighing the terms in the Method of Maximum Likelihood gives us a very flexible and useful way to improve the robustness of MLE. Till now the studies were focused mainly on the trimming factor. The theory of d-fullness gives us a powerful method to determine this property in the cases of WLTE, MLE and LTE. The aim of this study is to consider the weights of the WLTE estimators and to compare the results obtained by using different algorithms for calculating weights.

RISK FACTORS OF CENTRAL VENOUS CATHETER RELATED INFECTIONS IN INTENSIVE CARE PATIENTS
Dimitar Atanasov datanasov@fmi.uni-sofia.bg
D. Terziiski dterziiski@yahoo.com

1991 Mathematics Subject Classification: 62P10.
Key words: Central Venous Catheter (CVC) infection, Multivariate discriminant analysis.

This study investigates the incidence of and risk factors for Central Venous Catheter (CVC) infection in intensive care patients of Military Medical Academy in Sofia. CVCs were prospectively studied in patients who had lines inserted in general or neurosurgical intensive care and were expected to have the line in situ for at least 7 days. Catheters were cultured for CVC related infections and blood culture done when indicated. In 29% there is a CVC related infection and in 24.26% - a CVC related sepsis. After adjustment of duration of catheterization, independent predictors of CVC related infections were type of catheter, insertion site, sex, and Acute Physiology Chronic Health Evaluation (APACHE). Multivariate discriminant analysis was used in order to find out significantly important factors for CVC infection an sepsis. The variables entered into the model were those found to be statistically significant (p < 0.005) on multivariate analysis. The criterion for entering a variable into the model was the values of Mahalanobis statistics and the corresponding values of F-statistics. The software package use for statistical analysis was STATISTIKA 5.0.

RANDOMIZED PUSH-OUT MECHANISMS IN PRIORITY QUEUEING AND THEIR PROBABILITY CHARACTERISTICS
K. E. Avrachenkov
G. L. Shevlyakov
N. O. Vilchevski

1991 Mathematics Subject Classification: 60K25.
Key words: priority queueing disciplines, loss probabilities, mean queues.

The non-preemptive priority queueing with a finite buffer is considered. A randomized push-out buffer management mechanism that allows to control very efficiently the loss probability of priority packets is introduced. The packet loss probabilities for priority and non-priority traffic are derived with the use of the generating function approach. For the standard non-randomized push-out scheme, the explicit analytic expressions are obtained. A procedure for the numerical calculation of mean queues is also proposed.

AN APPLICATION OF ISO 5725 IN BREWING INDUSTRY
Plamen Mateev pmat@math.bas.bg
Dimitar Christozov dgc@aubg.bg

1991 Mathematics Subject Classification: 62P30, 62P10.
Key words: beer, alcohol chill haze, Test Chapon, colloidal stability, ISO 5725, Mandel`s statistics.

The colloidal stability is very important part of the total beer quality. The stabilized beers have to have a long shelf-life. Determination of some haze forming complexes could be very useful for prediction of beer colloidal stability. We study the repeatability and reproducibility of a method for determination of some haze forming complexes in beer. The method was tested in 10 laboratories. All of theme analyzed the same beer samples and carried out two measurements for each. Statistical evaluation of results was according ISO 5725 and previous experience. The applied ISO 5725 statistical analyzes ensured high quality and possibility of international recognition of the measurement method.

A STOCHASTIC APPROACH FOR INVESTIGATION ULTRAFAST PHENOMENA IN SEMICONDUCTORS
Todor V. Gurov gurov@copern.bas.bg
M. Nedjalkov mixi@iue.tuwien.ac.at

1991 Mathematics Subject Classification:65C05.
Key words: Monte Carlo algorithms.

In this paper a stochastic approach is proposed for investigation the ultrafast evolution of electrons interacting with phonons in the presence of an applied electric field. The quantum-kinetic equation describing the above ultrafast phenomena contains polynomial non-linearity which allows to use the link between non-stationary iterative processes and the branching stochastic processes. The considered stochastic approach relies on the numerical Monte Carlo (MC) theory as applied to the integral form of the quantum-kinetic equation and estimates the electron energy distribution using statistical averages over long evolution times. The numerical tests were performed for GaAs material parameters. The numerical results for the electron energy distribution function in the case of a non-linear electron quantum transport is compared with the obtained results in the linear case.

DIMENSION REDUCTION OF THE EXPLANATORY VARIABLES IN MULTIPLE LINEAR REGRESSION
P. Filzmoser P.Filzmoser@tuwien.ac.at
C. Croux

1991 Mathematics Subject Classification: 60C05, 62C20, 62C25.
Key words: multiple decisions, adaptation, exponential families, consistancy.

The asymptotic behavior of multiple decision procedures is studied when the underlying distributions depend on an unknown nuisance parameter. An adaptive procedure must be asymptotically optimal for each value of this nuisance parameter, and it should not depend on its value. A necessary and sufficient condition for the existence of such a procedure is derived. Several examples are investigated in detail, and possible lack of adaptation of the traditional overall maximum likelihood rule is discussed.

LOCAL-MEDIAN METHOD OF FORECASTING FOR REGRESSION TIME SERIES UNDER OUTLIERS
Yu. Kharin kharin@bsu.by
V. Maevskiy

1991 Mathematics Subject Classification: 62M20, 62-07, 62J05, 62P20.
Key words: Robustness, Forecasting, Regression, Outliers.

The local-median method of forecasting under the regression model with outliers is analyzed in this paper. The breakdown point is evaluated, the distribution function of the local-median forecast is given.

GENERALIZED SCALING FACTOR FOR ESTIMATING THE ACTIVITY CONCENTRATIONS OF DIFFICULT-TO-MEASURE NUCLIDES
Plamen Mateev pmat@math.bas.bg
Eugenia Stoimenova jeni@math.bas.bg

1991 Mathematics Subject Classification: 62P35, 62P30.
Key words: scaling factor, difficult-to-measure nuclides, statistical estimation.

Scaling factors represent the relationship between a crucial radionuclide concentration and other radionuclides concentrations. In this paper a generalization of the Scaling Factor Method is proposed.

DETECTING PRECIPITATION CLIMATE CHANGES: AN APPROACH BASED ON A STOCHASTIC DAILY PRECIPITATION MODEL
N. Neykov neyko.neykov@meteo.bg
P. Neytchev
W. Zucchini

1991 Mathematics Subject Classification: 62M10.
Key words:Binary time series, climate change, gamma time series, generalized linear models, Markov chain, rainfall modeling.

We consider development of daily precipitation models for some sites in Bulgaria. The precipitation process is modelled as a two-state first-order nonstationary Markov model. Both the probability of rainfall occurrance and the rainfall intensity are allowed depend on the intensity on the preceeding day. To investigate the existence of long-term trend and of changes in the pattern of seasonal variation we use a synthesis of the methodology presented in Grunwald and Jones (2000) and the idea behind the classical running windows technique for data smoothing. The resulting time series of model parameters are used to quantify changes in the precipitation process over the territory of Bulgaria.

MONTE CARLO STUDY OF PARTICLE TRANSPORT PROBLEM IN AIR POLLUTION
R.J. Papancheva rumi@cantor.bas.bg
Todor V. Gurov gurov@copern.bas.bg