Abstract
Consider a model with parameter = (, ), where is the parameter of interest, and let L(, ) denote the likelihood function. One approach to likelihood inference for is to use an integrated likelihood function, in which is eliminated from L(, ) by integrating with respect to a density function (|). The goal of this paper is to consider the problem of selecting (|) so that the resulting integrated likelihood function is useful for non-Bayesian likelihood inference. The desirable properties of an integrated likelihood function are analyzed and these suggest that (|) should be chosen by finding a nuisance parameter that is unrelated to and then taking the prior density for to be independent of . Such an unrelated parameter is constructed and the resulting integrated likelihood is shown to be closely related to the modified profile likelihood.
Original language | English (US) |
---|---|
Pages (from-to) | 524-542 |
Number of pages | 19 |
Journal | Biometrika |
Volume | 94 |
Issue number | 3 |
DOIs | |
State | Published - 2007 |
Keywords
- Modified profile likelihood
- Nuisance parameter
- Orthogonal parameters
- Reference prior
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Agricultural and Biological Sciences (miscellaneous)
- General Agricultural and Biological Sciences
- Statistics, Probability and Uncertainty
- Applied Mathematics