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Characterisation Of Linear Mini-Max Estimators For Loss Functions Of Arbitrary Power

Author

Listed:
  • K. HELMES

    (Institut für Operations Research, Humboldt — Universität zu Berlin, Spandauer Straße 1, 10178 Berlin, Germany)

  • C. SRINIVASAN

    (The Department of Statistics, College of Arts and Suences, University of Kentucky, Lexington, Kentucky, 40506-0027, USA)

Abstract

LetY(t),t∈[0,1], be a stochastic process modelled asdYt=θ(t)dt+dW(t), whereW(t)denotes a standard Wiener process, andθ(t)is an unknown function assumed to belong to a given setΘ⊂L2[0,1]. We consider the problem of estimating the valueℒ(θ), where ℒ is a continuous linear function defined on Θ, using linear estimators of the form =∫m(t)dY(t),m∈L2[0,1]. The distance between the quantityℒ(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.

Suggested Citation

  • K. Helmes & C. Srinivasan, 2001. "Characterisation Of Linear Mini-Max Estimators For Loss Functions Of Arbitrary Power," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 203-211.
    • Handle: RePEc:wsi:igtrxx:v:03:y:2001:i:02n03:n:s0219198901000397
    DOI: 10.1142/S0219198901000397
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    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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