VVS-SMS AiO lectures 2006

The section Mathematical Statistics organises special lecture afternoons where AiO's (Ph.D. students) who are close to finishing their theses, present their work. Previous SMS-VVS AiO afternoon have been held on 29 January 2004 and on 3 February 2005.

The afternoon is organised by the Korteweg-de Vries Institute for Mathematics of the Universiteit van Amsterdam under the auspices of the Section Mathematical Statistics (SMS) of the Dutch Society for Statistics and Operations Research (VVS)

Date and Location

Date:	January 26, 2006
Location:	Universiteit van Amsterdam, E building, Roetersstraat 11, Room E015
Travel directions:	From metro station Weesperplein, you walk to the East in Sarphatistraat (ascending numbers). After about 150 meters, you turn left into Roetersstraat, another 150 meters or so leads you to the entrance of the E building (Faculty of Economics and Econometrics). After having entered the main hall, look out for a big red clock, turn left when you are almost under it, and room E015 is within reach.

Speakers

Ramon van den Akker (UvT)
Ton Dieker (CWI)
Anne Fey (VU/Eurandom)
Thijs Vermaat (UvA/IBIS)

Programme

13.30-14.15	Anne Fey	Zhang's sandpile model
14.15-15.00	Ton Dieker	Fluid networks driven by a compound Poisson process
15.00-15.30		Coffee break
15.30-16.15	Ramon van den Akker	Asymptotic analysis of nearly unstable integer-valued autoregressive processes
16.15-17.00	Thijs Vermaat	Control charts in non-standard situations
17.00		Drinks

Abstracts

Ramon van den Akker: Asymptotic analysis of nearly unstable integer-valued autoregressive processes
This talk considers integer-valued autoregressive processes of order one, where the auto-regression parameter is close to unity. We consider the asymptotics of this `near unit root' situation. The local asymptotic structure of the likelihood ratios for the model is obtained, which shows that the limit experiment is not of the common LAQ type, but is instead Poissonian. This Poisson limit experiment is used to construct efficient estimation and testing procedures.

Ton Dieker: Fluid networks driven by a compound Poisson process
One of the cornerstones of queueing theory is the single-server queue, in which customers arrive to a system (counter, call center, elevator, or traffic light), possibly wait, and subsequently leave the system. However, for some applications (e.g., modern communication networks), individual customers are so small that they can hardly be distinguished. It is then easier to imagine a continuous stream of work that flows into the system. The resulting queueing model is called a fluid queue. In my talk, I address a model with several fluid queues in series, the so-called tandem fluid queue. Making use of the underlying Markovian structure, I show how the joint buffer-content distribution can be found.

Anne Fey: Zhang's sandpile model
The existing sandpile literature deals mainly with the abelian sandpile model (ASM). We treat a less known variant, Zhang's sandpile model. This model differs in two aspects from the ASM: First, additions are not discrete grains of sand, but random amounts with a uniform distribution. Second, if a site topples, it does not give one grain to each neighbor, but divides its entire content in equal amounts between its neighbors. Zhang conjectured that in the limit of infinite volume, his model tends to behave like an ASM. This belief is supported by simulations, but so far not by analytical investigations.
We have studied analytically the stationary distributions of this model in one dimension, for several cases of the addition distribution. Our main result is on the limit of infinitely many sites, for a nontrivial case. We find that the stationary distribution in that case indeed tends to that of the ASM.

Thijs Vermaat: Control charts in non-standard situations
In Statistical Process Control (SPC) we monitor a quality characteristic of a certain process. An example is the monitoring of the temperature in a glass furnace. When a large change in the temperature is signaled by a control chart, corrective actions in the process have to be made.
Traditionally, we assume that this quality characteristic follows a normal distribution and the subsequent observations in time are independent. The first problem is that the quality characteristic is no longer normally distributed. We present two possible solutions: a non-parametric, and a semi-Bayesian approach. The second problem is that the observations are serially correlated. I will develop a modified Exponentially Weighted Moving Average (EWMA) control chart which is adapted for serial correlation.