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The theory of estimating equations is developed in this chapter. Estimating equations are a generalization of the maximum likelihood method and the method of moments, and have their combined flavors and advantages. Estimating equations are the basic components for Quasi Likelihood, Generalized Linear Models, Generalized Estimating Equations, and Generalized Method of Moments, which have wide applications. In addition, estimating equations also provide a convenient theoretical framework to develop many aspects of statistical inference, such as conditional inference, inference in the presence of nuisance parameters, efficient estimation, and the information bounds. They make some optimal results in statistical inference transparent via projections in Hilbert spaces.
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