A linear mini-max estimator for the case of a quartic loss function

K. Helmes, C. Srinivasan

Research output: Contribution to journalArticlepeer-review


Let Y(t) be a stochastic process on [0,1] modeled 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 O L 2[0,1]. We consider the problem of estimating the value L(θ), where L is a known continuous linear function defined on O, using linear estimators of the form (m,y) = m(t) dY(t)j m ε L [0,1]. We solve the problem for the case of a quartic loss function, and compare the solution of the quartic case with the solution for the case of a quadratic loss function.

Original languageEnglish
Pages (from-to)343-364
Number of pages22
JournalRandom Operators and Stochastic Equations
Issue number4
StatePublished - Jan 2000

Bibliographical note

Funding Information:
Supported in part by NSF Grant

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability


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