is a $p$-vector of zeros. Prominent examples of estimation methods that fall within the above framework are estimation via quasi likelihoods [@wedderburn:1974] and generalized estimating equations [@liang+zeger:1986]. @stefanski+boos:2002 provide an accessible overview of estimating functions and demonstrate their generality and ability to tackle challenging estimation problems with fewer assumptions than likelihood-based estimation requires.

One way to derive estimating equations is through a, typically stronger, modelling assumption that ${{}Y}_i$ has a distribution function $F_i({{}y}_i | {{}x}_i, {{}\theta})$. The estimator $\hat{{}\theta}$ can then be taken to be the maximizer of the objective function $$\label{objective_function}
  l({{}\theta}) = \sum_{i =1}^k \log f_i({{}y}_i | {{}x}_i, {{}\theta}) \, ,$$ where $f_i({{}y}_i | {{}x}_i, {{}\theta})$ is the mixed joint density corresponding to $F_i({{}y}_i | {{}x}_i, {{}\theta})$. The word “mixed” is used here to allow for the fact that some of the components of ${{}y}_i$ may be continuous and some others may be discrete. If the objective function (\[objective\_function\]) is used, then the estimating functions in (\[estimating\_eqautions\]) have ${{}\psi}^i({{}\theta}) = \nabla \log f_i({{}y}_i | {{}x}_i,
{{}\theta})$, assuming that the gradient exists in $\Theta$. Prominent examples of estimation methods that involve an objective function of the form (\[objective\_function\]) are maximum likelihood and maximum composite likelihood [see, for example, @lindsay:1988; 