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 Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Empirical Likelihood Ratio Confidence Intervals for a Single Functional

Art B. Owen
Biometrika
Vol. 75, No. 2 (Jun., 1988), pp. 237-249
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2336172
Stable URL: http://www.jstor.org/stable/2336172
Page Count: 13
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Empirical Likelihood Ratio Confidence Intervals for a Single Functional
Preview not available

Abstract

The empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken. In this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions. It is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean, for a class of M-estimates that includes quantiles, and for differentiable statistical functionals. The results are nonparametric extensions of Wilks's (1938) theorem for parametric likelihood ratios. The intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on Student's t statistic. A hybrid method that used the bootstrap to determine critical values of the likelihood ratio is introduced.

Page Thumbnails

  • 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
  • Thumbnail: Page 
245
    245
  • Thumbnail: Page 
246
    246
  • Thumbnail: Page 
247
    247
  • Thumbnail: Page 
248
    248
  • Thumbnail: Page 
249
    249