Access

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

Local Sufficiency

Peter McCullagh
Biometrika
Vol. 71, No. 2 (Aug., 1984), pp. 233-244
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2336239
Stable URL: http://www.jstor.org/stable/2336239
Page Count: 12
  • Read Online (Free)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Local Sufficiency
Preview not available

Abstract

Non-Bayesian inference is considered for a scalar parameter θ based on a p-dimensional statistic X which need not constitute a sufficient reduction of the original data. It is shown that there exists a (p - 1)-dimensional statistic A that is jointly second-order locally ancillary for θ near θ0 but that, for $p > 2, A$ is not unique even up to nonsingular transformations. To avoid any ambiguity in the resulting inferences, we show that there exists a statistic S, to be called second-order locally sufficient, that is, to second order, independent of any second-order locally ancillary statistic A. Furthermore, S is unique up to a nonsingular transformation, is easily computed from the log likelihood ratio statistic, has a simple distribution and avoids the perplexing problem of specifying the appropriate conditioning statistic. Confidence limits based on S have the desired coverage probability conditionally on any A, and therefore unconditionally, with error O(n-1) in each tail. Finally, for vector-valued θ, we give a rather general proof of Barndorff-Nielsen's (1980) formula for the conditional distribution of θ̂.

Page Thumbnails

  • Thumbnail: Page 
233
    233
  • Thumbnail: Page 
234
    234
  • Thumbnail: Page 
235
    235
  • Thumbnail: Page 
236
    236
  • Thumbnail: Page 
237
    237
  • Thumbnail: Page 
238
    238
  • Thumbnail: Page 
239
    239
  • Thumbnail: Page 
240
    240
  • Thumbnail: Page 
241
    241
  • Thumbnail: Page 
242
    242
  • Thumbnail: Page 
243
    243
  • Thumbnail: Page 
244
    244