Minimax estimation in the blurred signal model

E. Belitser

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    Abstract

    We study problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise. The unknown function is assumed to belong to an ellipsoid in L_2([0,1]). We propose a linear estimator and show that its maximal risk, under some conditions, has the same asymptotic behavior as the minimax risk. We also derive the exact asymptotics of the minimal risk. The results are illustrated by one example.
    Original languageEnglish
    Title of host publicationProbability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998)
    EditorsB. Grigelionis, J. Kubilius, V. Paulauskas, H. Pragarauskas, R. Rudzkis, V. Statulevicius
    Place of PublicationVilnius
    PublisherTEV
    Pages57-66
    ISBN (Print)9986-546-72-9
    Publication statusPublished - 1999

    Fingerprint

    Minimax Estimation
    Minimax Risk
    Linear Estimator
    Additive Noise
    Ellipsoid
    Asymptotic Behavior
    Unknown
    Model

    Cite this

    Belitser, E. (1999). Minimax estimation in the blurred signal model. In B. Grigelionis, J. Kubilius, V. Paulauskas, H. Pragarauskas, R. Rudzkis, & V. Statulevicius (Eds.), Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998) (pp. 57-66). Vilnius: TEV.
    Belitser, E. / Minimax estimation in the blurred signal model. Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998). editor / B. Grigelionis ; J. Kubilius ; V. Paulauskas ; H. Pragarauskas ; R. Rudzkis ; V. Statulevicius. Vilnius : TEV, 1999. pp. 57-66
    @inproceedings{ccf2913ab48d498e948aa2e552134629,
    title = "Minimax estimation in the blurred signal model",
    abstract = "We study problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise. The unknown function is assumed to belong to an ellipsoid in L_2([0,1]). We propose a linear estimator and show that its maximal risk, under some conditions, has the same asymptotic behavior as the minimax risk. We also derive the exact asymptotics of the minimal risk. The results are illustrated by one example.",
    author = "E. Belitser",
    year = "1999",
    language = "English",
    isbn = "9986-546-72-9",
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    editor = "B. Grigelionis and J. Kubilius and V. Paulauskas and H. Pragarauskas and R. Rudzkis and V. Statulevicius",
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    Belitser, E 1999, Minimax estimation in the blurred signal model. in B Grigelionis, J Kubilius, V Paulauskas, H Pragarauskas, R Rudzkis & V Statulevicius (eds), Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998). TEV, Vilnius, pp. 57-66.

    Minimax estimation in the blurred signal model. / Belitser, E.

    Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998). ed. / B. Grigelionis; J. Kubilius; V. Paulauskas; H. Pragarauskas; R. Rudzkis; V. Statulevicius. Vilnius : TEV, 1999. p. 57-66.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    TY - GEN

    T1 - Minimax estimation in the blurred signal model

    AU - Belitser, E.

    PY - 1999

    Y1 - 1999

    N2 - We study problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise. The unknown function is assumed to belong to an ellipsoid in L_2([0,1]). We propose a linear estimator and show that its maximal risk, under some conditions, has the same asymptotic behavior as the minimax risk. We also derive the exact asymptotics of the minimal risk. The results are illustrated by one example.

    AB - We study problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise. The unknown function is assumed to belong to an ellipsoid in L_2([0,1]). We propose a linear estimator and show that its maximal risk, under some conditions, has the same asymptotic behavior as the minimax risk. We also derive the exact asymptotics of the minimal risk. The results are illustrated by one example.

    M3 - Conference contribution

    SN - 9986-546-72-9

    SP - 57

    EP - 66

    BT - Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998)

    A2 - Grigelionis, B.

    A2 - Kubilius, J.

    A2 - Paulauskas, V.

    A2 - Pragarauskas, H.

    A2 - Rudzkis, R.

    A2 - Statulevicius, V.

    PB - TEV

    CY - Vilnius

    ER -

    Belitser E. Minimax estimation in the blurred signal model. In Grigelionis B, Kubilius J, Paulauskas V, Pragarauskas H, Rudzkis R, Statulevicius V, editors, Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998). Vilnius: TEV. 1999. p. 57-66