Find ξ Value with Maximum Likelihood

[ryusukekenji]

http://bbs.mathchina.com/usr1PvjRWKew/4/22/graph_1261406609.jpg

I can't understand the equation, may I know is there any good idea to get the value of ξ?

 

[SW VandeCarr]

It is a little hard to read, but based on the curve and the Fig 1 label underneath , it looks like the values of $$\xi$$are plotted on the horizontal axis.

 

[ryusukekenji]

http://cos.name/bbs/attachment/Mon_0912/15_88059_ae128f170c6c431.jpg

φ=non-increase function
tk=Time of observation k
I have built up may basic model, while just leaving decay speed ζ which I have no idea...

 

[SW VandeCarr]

Sorry. I didn't know you wanted to derive a value for a parameter of $$\xi$$. I took $$\xi$$ as given and thought we were asking about Maximum Likelihood Estimation.

 

[ryusukekenji]

I didnt stated whole model at first, that's why...
hmmm... It must apply Maximum Likelihood in order to get ζ ... but I am not really understand α and β which are probabilities of occurrence.

 

[HallsofIvy]

You still haven't told us what the problem really is! If it is to find the maximum likliehood estimator of $\zeta$ from the graph, then it looks to me like the maximum value on the graph occurs around $\zeta= 0.006$.

 

[ryusukekenji]

Example：

T1 T2 X Y Date
A B 1 0 01Jan
A C 2 2 03Jan
B D 3 1 03Jan
A D 1 1 08Jan
B C 0 0 08Jan
C B 2 1 09Jan
D A 1 0 14Jan
D B 2 3 15Jan
C A 2 1 15Jan
B A 1 1 18Jan

I have a dataset of observations on robot soccer competition. Right here I try to stated example above if let say I would like to count team scoring ability through individual double poisson with time series. Previous matches result will less effect through decay function.
The picture above is one of my reference, I would like to follow this paper's weighting function but I am not really know how to get the maximum likelihood of decay rate ζ.