and estimate u from the likelihood function: 
L = I Na (?;, u) 2 max; u estimator for u (2) 
This formulation is - within the classical theory of Maximum Likelihood - 
only justified if 7, :N,. This latter condition is obviously not truo, 
considering the outlyers in Z,. So we have to reinterprete the Maximum 
Likelihood Method, in that: 
We estimate U; only from there measurements Z;, which are sufficiently 
clustered around a central value, E(Z): 
2 i 2Na(Z ;; E(Z), a) jtí (3) 
4.  DERIVATION OF SOLUTION 
Taking the logarithm of (2), we obtain: 
F(û) = 1nL = Eln Ne (Z;,û) => min, (4) 
or with #(Z;) = - In Na(Z;) 
F(4) = I#(Z;) => min . (5) 
with $(Z;) = (Z, m E(Z,)) for (Zi - E(Z;)) (a 
R else; R = » (6) 
The function (5) is a semi-convex function, and if the constant a is chosen 
sufficiently large there exists a unique vector ü, for which it holds: 
F(û) « F(v) for all v. 
The estimation problem (5), (6) can now be solved by conventional methods 
of nonlinear programming/optimization. 
The information matrix (Wilks, 1962) for û is equal to: 
ô21nL 
1(1,3) = > ECS, 64 
) 
Assuming validity of our argument (3), this information matrix is equal to, 
(Kubik, 1970): 
I = B'PB 
with P being a diaponal matrix: 
a for (Z, = E(Z,)) <a 
PCI, = 
050 o for (2, - E(Z,)) > a 
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