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3. The Estimation Process

The estimation process is splitted in two phases -- the Pilot and the Main ones.

At the Pilot Phase, the code performs a prescribed number of pilot simulations; these pilot simulations are partitioned in prescribed number of groups of equal size. As a result, the code specifies a reference parameter vector v₀, of the same structure as the actual parameter vector v. In what follows, f(y,v) means the actual pdf of the state vector, and f(y,v₀) is the reference pdf of the state vector, i.e., the distribution of the same type with v₀ playing the role of v.

At the Main Phase, the code uses the reference parameter vector to build a Likelihood Ratio estimate of the expected performance:

, where

N is the number of simulations at the Main Phase

{Y¹,Y²,...Y^N} is an independent sample of state vectors taken from the reference distribution with pdf f(y,v₀)

is the density of the distribution f(y,v) w.r.t. distribution f(y,v₀) (it is called a likelihood ratio).

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