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- W6075650 abstract "Assume that we can control an input x n ∈ C ⊂ R, and observe an output y n such that y n (x n ) = f(x n ) + c n , where the e n are independent with E(∈ n ) = 0 and Var(∈n) = σ2. The function E(y|x) = f(x) is unknown, continuous and in our examples it will belong to a parametric family f(x;s), known up to a vector s of unknown parameters with a prior distribution G 0(s). We assume that there is a unique θ such that f(θ) = T, where T is a known target and f′ (θ) > 0. By subtracting T from each y n (x n ) we can take T to be 0. There is a rich literature on sequential designs for estimating the root θ of an unknown equation evaluated with noise; good references are Wu (1986) and Frees and Ruppert (1990). This paper adapts some of these designs to problems that involve a small number of observations AT, and cover the whole range that goes from the purely root estimation problem to stochastic control problems where the goal is to keep the N responses as close to T as possible." @default.
- W6075650 created "2016-06-24" @default.
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- W6075650 date "1996-01-01" @default.
- W6075650 modified "2023-09-23" @default.
- W6075650 title "Small Sequential Designs that Stay Close to a Target" @default.
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- W6075650 doi "https://doi.org/10.1007/978-3-642-46992-3_32" @default.
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