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.

Maximum Likelihood in Small Samples: Estimation in the Presence of Nuisance Parameters

D. A. Sprott
Biometrika
Vol. 67, No. 3 (Dec., 1980), pp. 515-523
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2335119
Stable URL: http://www.jstor.org/stable/2335119
Page Count: 9
  • 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.
Maximum Likelihood in Small Samples: Estimation in the Presence of Nuisance Parameters
Preview not available

Abstract

The paper discusses various pivotal quantities associated with the application of maximum likelihood to small samples to estimate a parameter θ1 in the presence of other unknown parameters θ2,...,θk. This extends the previous work of Sprott (1973, 1975). The criterion of normality of the relative likelihood, applicable to the single parameter case, is here replaced by the normality of the relative likelihood maximized over θ2,...,θk. This gives a more objective criterion for the application of standard maximum likelihood methods to estimate θ1 than merely the numerical size of the sample. As for the single parameter case, it is necessary to emphasize that the normality of the maximum relative likelihood need not entail, nor be entailed by, a large sample size; it requires expressing the problem, if possible, in terms of a parameter φ = φ(θ1), the maximum relative likelihood of which is approximately normal. Comparisons with exact results are given. But the practicality of such methods arises in more complicated cases when exact solutions are not easily available.

Page Thumbnails

  • Thumbnail: Page 
515
    515
  • Thumbnail: Page 
516
    516
  • Thumbnail: Page 
517
    517
  • Thumbnail: Page 
518
    518
  • Thumbnail: Page 
519
    519
  • Thumbnail: Page 
520
    520
  • Thumbnail: Page 
521
    521
  • Thumbnail: Page 
522
    522
  • Thumbnail: Page 
523
    523