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Quadratic Artificial Likelihood Functions Using Estimating Functions

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  • 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.

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  • Jinfang Wang, 2006. "Quadratic Artificial Likelihood Functions Using Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 379-390, June.
    • Handle: RePEc:bla:scjsta:v:33:y:2006:i:2:p:379-390
    DOI: 10.1111/j.1467-9469.2006.00480.x
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