[Statlist] Seminar ueber Statistik

[Christina Kuenzli]

                       ETH and University of Zurich 
      Proff. A.D. Barbour -- P. Buehlmann -- F. Hampel -- H.R. Kuensch 

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            We are pleased to announce the following talk
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Friday, November 26, 2004, 15.15 h, LEO C 15
       
      Juhyun Park, University of Zurich 

      Nonparametric inference based on indirect measurement
 
We consider a statistical inference problem in an infinite server
queuing system, called an $M/G/\infty$ model. A simple description
appears as Poisson arrival customers whose service time follows a
general distribution. There are infinite number of servers in the
system and depending on whether or not a customer is present, the
system is alternating the two states, busy and idle. This is a
well known queuing model that has been used in various contexts in
disguise. We briefly introduce our motivation from internet
traffic modeling framework.

Our primary interest in this model is the service time
distribution. To be more informative we are particularly
interested in the shape of the distribution or the density
function. Often times however we do not have a direct access to
the service times and only the information about busy/idle periods
is available. Although the model has been used and studied in
various contexts, not many work has been done in that direction
with such limited information.

The relationship between busy periods and service times is known
through the Laplace transform of the busy periods. Thus this can
be viewed as an inversion problem, for which the solution usually
is obtained by taking a numerical approximation scheme. Here we
adopt a statistical nonparametric approach. We use an expansion
idea to exploit the Laplace transform. This enables us to find an
explicit inversion formula to recover the service time
distribution. This idea is extended to find the density function.
Based on that we propose nonparametric estimators with the busy
period distribution replaced by its empirical distribution. In
particular, the density estimation involves a conventional kernel
smoothing estimator whose properties are well known. Theoretical
properties of both estimators are studied. We also discuss
monotonicity of the distribution function estimator and further
incorporate a monotonizing scheme if necessary. Performance issues
of the estimators are examined through a simulation study in which
both unimodal and bimodal densities are considered.
              
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Further information: Christina Kuenzli, Statistics Seminar of ETH Zurich 
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Everybody is kindly invited
 
Eidgenoessische Technische Hochschule Zuerich
Swiss Federal Insitute of Technology Zurich

________________________________________________________
Christina Kuenzli            <kuenzli using stat.math.ethz.ch>
Seminar fuer Statistik      
Leonhardstr. 27,  LEO D11          phone: +41 1 632 3438         
ETH-Zentrum,                       fax  : +41 1 632 1228 
CH-8092 Zurich, Switzerland        http://stat.ethz.ch/~