
78 Modeling and In verse Problems in the Presence of Uncertainty
arguments. However, we are only interested in behavior as N → ∞. If we as-
sume only that the
e
E
j
are independent and identically distributed with constant
variance (as is commonly the case), the Central Limit Theorem (i.e., Theo-
rem 2.6.2) applies and the distribution (whether chi-squared or not) will ten d
toward the normal. Even in the more general case of non-cons tant variance,
a simple change of variables can be used to reduce to the constant variance
case. Hence we really only need the variance terms to be bounded above.
Next, consider only a single element , θ
N
l
, of the estimator. ...