Nested Monte Carlo
= Nested Monte Carlo
<Nested Monte Carlo> approximates an outer <expected value> whose integrand contains another <expected value>. A nonlinear transformation, such as a <logarithm>, of an inner sample average usually introduces finite-sample bias. Increasing both sample sizes requires suitable integrability controls to establish consistency; an <unbiased estimator> of the inner quantity does not make its <logarithm> unbiased.