Simulation input modeling: a kernel approach to estimating the density of a conditional expectation
Proceedings of the 35th conference on Winter simulation: driving innovation
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To estimate the density f of a conditional expectation μ(Z) = E[X|Z], Steckley and Henderson (2003) sample independent copies Z1,..., Zm; then, conditional on Zi, they sample n independent samples of X, and their sample mean Xi is an approximate sample of μ(Zi). For a kernel density estimate f of f based on such samples and a bandwidth (smoothing parameter) h, they consider the mean integrated squared error (MISE), ∫(f (x).. f (x))2dx, and find rates of convergence of m, n and h that optimize the rate of convergence of MISE to zero. Inspired by the cross-validation approach in classical density estimation, we develop an estimate of MISE (up to a constant) and select the h that minimizes this estimate. While a convergence analysis is lacking, numerical results suggest that our method is promising.