@varin+reid+firth:2011].

Assumptions
-----------

The assumptions we employ for the theoretical development in this work are listed below.

1.  \[consistency\] Consistency: $$\hat{{}\theta} \stackrel{p}{\longrightarrow} \bar{{{}\theta}} \, ,$$ where $\bar{{{}\theta}}$ is such that $\expect_G ({{}\psi}^i) = {{}0}_p$ for all $i \in \{1, \ldots, k\}$, with ${{}\psi}^i={{}\psi}^i(\bar{{}\theta})$ and $\expect_G(\cdot)$ denoting expectation with respect to the unknown joint distribution function $G$. In particular, we assume that $\hat{{}\theta} - \bar{{{}\theta}} = O_p(n^{-1/2})$, where $n \equiv n(k, m, q)$ is a measure of information about ${{}\theta}$.

2.  \[smoothness\] Smoothness: The derivatives of $\psi_r^i({{}\theta})$ exist up to the $5$-th order. In particular, $$l_{R_a}({{}\theta}) = \sum_{i=1}^k \frac{\partial^{a-1}
          \psi_{r_1}^i({{}\theta})}{\partial {{}\theta}^{r_2} \cdots \partial
          {{}\theta}^{r_a}} \, ,$$ exist for any set $R_a = \{r_1, \ldots, r_a\}$, with $r_j \in \{1, \ldots, p\}$ and $a \in \{1, \ldots, 5\}$, under the convention that $l_r({{}\theta}) = \sum_{i = 1}^k \psi_r^i({{}\theta})$ and that the components of ${}\theta$ are identified by superscripts.

3.  \[derivative\_orders\] Asymptotic orders of centred estimating function derivatives: $$H_{R_a} = l_{R_a} - \mu_{R_a} = O_p(n ^{1/2}) \, ,$$ where $\mu_{R_a} = \expect_G(l_{R_a})$, $l_{R_a} = l_{R_a}(\bar{{}\theta})$ and $\mu_{R_a} = \mu_{R_a}(\bar{{}\theta})$ exist for $a \in \{1, \ldots, 5\}$.

4.  \[moment\_orders\] Asymptotic orders of joint central moments of estimating functions and their derivatives: $$\nu_{R_{a_1}, S_{a_2}, \ldots, 