Statistical Science

Inference Based on Estimating Functions in the Presence of Nuisance Parameters

Kung-Yee Liang and Scott L. Zeger

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Abstract

In many studies, the scientific objective can be formulated in terms of a statistical model indexed by parameters, only some of which are of scientific interest. The other "nuisance parameters" are required to complete the specification of the probability mechanism but are not of intrinsic value in themselves. It is well known that nuisance parameters can have a profound impact on inference. Many approaches have been proposed to eliminate or reduce their impact. In this paper, we consider two situations: where the likelihood is completely specified; and where only a part of the random mechanism can be reasonably assumed. In either case, we examine methods for dealing with nuisance parameters from the vantage point of parameter estimating functions. To establish a context, we begin with a review of the basic concepts and limitations of optimal estimating functions. We introduce a hierarchy of orthogonality conditions for estimating functions that helps to characterize the sensitivity of inferences to nuisance parameters. It applies to both the fully and partly parametric cases. Throughout the paper, we rely on examples to illustrate the main ideas.

Article information

Source
Statist. Sci. Volume 10, Number 2 (1995), 158-173.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.ss/1177010028

Digital Object Identifier
doi:10.1214/ss/1177010028

Mathematical Reviews number (MathSciNet)
MR1368098

Zentralblatt MATH identifier
0955.62558

JSTOR
links.jstor.org

Citation

Liang, Kung-Yee; Zeger, Scott L. Inference Based on Estimating Functions in the Presence of Nuisance Parameters. Statist. Sci. 10 (1995), no. 2, 158--173. doi:10.1214/ss/1177010028. http://projecteuclid.org/euclid.ss/1177010028.


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See also

  • See Comment: V. P. Godambe. [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Comment. Statist. Sci., Volume 10, Number 2 (1995), 173--174.
  • See Comment: Bruce G. Lindsay, Bing Li. [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Comment. Statist. Sci., Volume 10, Number 2 (1995), 175--177.
  • See Comment: Peter McCullagh. [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Comment. Statist. Sci., Volume 10, Number 2 (1995), 177--179.
  • See Comment: George Casella, Thomas J. DiCiccio, Martin T. Wells. [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Comment: Alternative Aspects of Conditional Inference. Statist. Sci., Volume 10, Number 2 (1995), 179--185.
  • See Comment: A. P. Dawid, C. Goutis. [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Comment. Statist. Sci., Volume 10, Number 2 (1995), 185--186.
  • See Comment: Thomas A. Severini. [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Comment. Statist. Sci., Volume 10, Number 2 (1995), 187--189.
  • See Comment: Louise M. Ryan. [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Comment. Statist. Sci., Volume 10, Number 2 (1995), 189--193.
  • See Comment: N. Reid. [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Rejoinder. Statist. Sci., Volume 10, Number 2 (1995), 193--196.
  • See Comment: Kung-Yee Liang, Scott L. Zeger. [Inference Based on Estimating Functions in the Presence of Nuisance Parameters]: Rejoinder. Statist. Sci., Volume 10, Number 2 (1995), 196--199.