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- Title
Characterisation of Linear Mini-Max Estimators for Loss Functions of Arbitrary Power.
- Authors
Helmes, K.; Srinivasan, C.
- Abstract
Let Y(t), t ∈ [0, 1], be a stochastic process modelled as dYt = θ(t)dt + dW(t), where W(t) denotes a standard Wiener process, and θ(t) is an unknown function assumed to belong to a given set ... ⊂ L² [0, 1]. We consider the problem of estimating the value ...(θ), where ... is a continuous linear function defined on ..., using linear estimators of the form 〈m, y〉 = ∫ m(t)dY(t), m ∈ L² [0,1]. The distance between the quantity ...(θ) and the estimated value is measured by a loss function. In this paper, we consider the loss function to be an arbitrary even power function. We provide a characterisation of the best linear mini-max estimator for a general power function which implies the characterisation for two special cases which have previously been considered in the literature, viz. the case of a quadratic loss function and the case of a quartic loss function.
- Subjects
LINEAR systems; ESTIMATION theory
- Publication
International Game Theory Review, 2001, Vol 3, Issue 2/3, p203
- ISSN
0219-1989
- Publication type
Article
- DOI
10.1142/S0219198901000397