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- Title
Quadratic Artificial Likelihood Functions Using Estimating Functions.
- Authors
JINFANG WANG
- Abstract
A vector-valued estimating function, such as the quasi-score, is typically not the gradient of any objective function. Consequently, an analogue of the likelihood function cannot be unambiguously defined by integrating the estimating function. This paper studies an analogue of the likelihood inference in the framework of optimal estimating functions. We propose a quadratic artificial likelihood function for an optimal estimating function. The objective function is uniquely identified as the potential function from the vector field decomposition by imposing some natural restriction on the divergence-free part. The artificial likelihood function is shown to resemble a genuine likelihood function in a number of respects. A bootstrap version of the artificial likelihood function is also studied, which may be used for selecting a root as an estimate from among multiple roots to an estimating equation.
- Subjects
VECTOR analysis; ESTIMATION theory; PARTIAL differential equations; STOCHASTIC processes; MATHEMATICAL statistics
- Publication
Scandinavian Journal of Statistics, 2006, Vol 33, Issue 2, p379
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2006.00480.x