If you need an accessible version of this item please contact JSTOR User Support

Modulation of Estimators and Confidence Sets

Rudolf Beran and Lutz Dumbgen
The Annals of Statistics
Vol. 26, No. 5 (Oct., 1998), pp. 1826-1856
Stable URL: http://www.jstor.org/stable/120023
Page Count: 31
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Modulation of Estimators and Confidence Sets
Preview not available

Abstract

An unknown signal plus white noise is observed at n discrete time points. Within a large convex class of linear estimators of ξ , we choose the estimator ξ̂ that minimizes estimated quadratic risk. By construction, ξ̂ is nonlinear. This estimation is done after orthogonal transformation of the data to a reasonable coordinate system. The procedure adaptively tapers the coefficients of the transformed data. If the class of candidate estimators satisfies a uniform entropy condition, then ξ̂ is asymptotically minimax in Pinsker's sense over certain ellipsoids in the parameter space and shares one such asymptotic minimax property with the James-Stein estimator. We describe computational algorithms for ξ̂ and construct confidence sets for the unknown signal. These confidence sets are centered at ξ̂, have correct asymptotic coverage probability and have relatively small risk as set-valued estimators of ξ .

Page Thumbnails

  • Thumbnail: Page 
1826
    1826
  • Thumbnail: Page 
1827
    1827
  • Thumbnail: Page 
1828
    1828
  • Thumbnail: Page 
1829
    1829
  • Thumbnail: Page 
1830
    1830
  • Thumbnail: Page 
1831
    1831
  • Thumbnail: Page 
1832
    1832
  • Thumbnail: Page 
1833
    1833
  • Thumbnail: Page 
1834
    1834
  • Thumbnail: Page 
1835
    1835
  • Thumbnail: Page 
1836
    1836
  • Thumbnail: Page 
1837
    1837
  • Thumbnail: Page 
1838
    1838
  • Thumbnail: Page 
1839
    1839
  • Thumbnail: Page 
1840
    1840
  • Thumbnail: Page 
1841
    1841
  • Thumbnail: Page 
1842
    1842
  • Thumbnail: Page 
1843
    1843
  • Thumbnail: Page 
1844
    1844
  • Thumbnail: Page 
1845
    1845
  • Thumbnail: Page 
1846
    1846
  • Thumbnail: Page 
1847
    1847
  • Thumbnail: Page 
1848
    1848
  • Thumbnail: Page 
1849
    1849
  • Thumbnail: Page 
1850
    1850
  • Thumbnail: Page 
1851
    1851
  • Thumbnail: Page 
1852
    1852
  • Thumbnail: Page 
1853
    1853
  • Thumbnail: Page 
1854
    1854
  • Thumbnail: Page 
1855
    1855
  • Thumbnail: Page 
1856
    1856