Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

Adaptive Estimation of Monotone Functions

  • Kang, Yung-Gyung (Department of Computer Science and Statistics, Hanshin University)
  • Published : 1998.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

In the white noise model we construct an adaptive estimate for f(0) for a decreasing function f. We also show that the maximum mean square error of this estimate attains the same rate as the minimax risk simultaneously over a range of Lipschitz classes of order less than or equal to one.

Keywords

References

  1. Statistical inference under order restrictions Barlow, R. E.;Bartholomew, D. J.;Bremner, J. M.;Brunk, H. D.
  2. Annals of Statistics v.24 Asymptotic equivalence of nonparametric re-gression and white noise Brown, L.;Low, M.
  3. Annals of Statistics v.24 A constrained risk inequality with applications to nonparametric functional estimation Brown, L.;Low, M.
  4. Annals of Statistics v.19 Geometrizing rates of convergence, Ⅲ Donoho, D.L.;Liu, R.c.
  5. Technometrics v.26 The monotone smoothing of scatter-plots Friedman, J.;Tibshirani, R.
  6. Skand. Aktuarietidskr v.39 On the theory of mortality measurement, Ⅱ Grenander, U.
  7. Contributions to Mathematical Econimics Hildenbrand, K.;Hildenbrand, W.(ed.);A. Mas-Colell(ed.)
  8. Theory of Probability and its Application v.29 On nonparametric estimation of the value of a linear functional in Gaussian White noise Ibragimov, I.A.;Hasminskii, R.Z.
  9. Biometrics v.46 Monotone smoothing with application to dose-response curves and the assessment of synergism Kelly, C.;Rice, J.
  10. Statistics and probability : Essay in honor of C. R. Rao Kiefer, J.;Kallianpur, G.(ed.);Krishnaiah, P. R.(ed.);Ghosh, J. K(ed.)
  11. Theory of Probability and its Application v.35 On a problem of adaptive estimation in Gaussian White noise Lepskii, O. V.
  12. Advances in Sovient Mathematics v.12 On a problem of adaptive estimation in Gaussian White noise Lepskii, O. V.
  13. Annals of Statistics v.20 Renormalization and white noise approximation for non-parametric functional estimation problems Low, M.G.
  14. Annals of Statistics v.23 Bias-variance tradeoffs in functional estimation problems Low, M.G.
  15. Annals of Statistics v.19 Estimating a smooth monotone regression function Mammen, E.
  16. Annals of Statistics v.24 Asymptotic equivalence of density estimation and Gaus-sian white noise Nussbaum, M.
  17. Problems Inform. Transmission v.16 Optimal filtering of square integrable signals in Gaussian white noise Pinsker, M.S.
  18. Science v.243 Earthquake hazard after a main shock in southern california Reasenberg, P. A.;Jones, L. M.
  19. Economics, 12th ed. Samuelson, P.;Nordhaus, W.