6Estimation Theory
In statistical signal processing, the observations from each experiment are modeled as function of parameters θ that can be either deterministic, or random, or any combination:
where each observation of the set {x[i]} can have arbitrary size 
. Another common situation is the presence of additive noise in observations
The purpose of estimation theory is to infer the value of a limited number of p parameters θ that model the signal component from a judicious analysis of the set 
, where subscript N is only to highlight the number of independent experiments, but not the way these are ordered into xN (column‐wise, row‐wise, matrix, etc.) The estimator is any transformation (in general, non‐linear and/or implicitly defined)
that manipulates the observations xN to have an estimate of θ according to some criteria. In addition, since xN is an rv (usually multivariate), the estimate itself is an rv and metrics evaluate how good/bad an estimator is.
6.1 Historical Notes ...
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