The basis of the method is to have, or to find, a set of simultaneous equations involving both the sample data and the unknown model parameters which are to be solved in order to define the estimates of the parameters.[1] Various components of the equations are defined in terms of the set of observed data on which the estimates are to be based.
Suppose that a sample of data is available from which either the sample mean, , or the sample median, m, can be calculated. Then an estimating equation based on the mean is
while the estimating equation based on the median is
Each of these equations is derived by equating a sample value (sample statistic) to a theoretical (population) value. In each case the sample statistic is a consistent estimator of the population value, and this provides an intuitive justification for this type of approach to estimation.
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Heyde, Christopher C. (1997). Quasi-Likelihood and Its Application: A General Approach to Optimal Parameter Estimation. New York: Springer-Verlag. ISBN0-387-98225-6.
McLeish, D. L.; Small, Christopher G. (1988). The Theory and Applications of Statistical Inference Functions. New York: Springer-Verlag. ISBN0-387-96720-6.
Small, Christopher G.; Wang, Jinfang (2003). Numerical Methods for Nonlinear Estimating Equations. New York: Oxford University Press. ISBN0-19-850688-0.