An asymptotic expansion for the distribution of the least squares estimator of the non-linear regression parameter

For a one-dimensional parameter non-linear regression model
$$ x_j=g_j(\theta_0)+\varepsilon_j,\qquad j\ge 1, $$
under some assumptions about the non-random sequence $\{g_j(\theta_0)\}_{j\ge 1}$ and the random sequence $\{\varepsilon_j\}_{j\ge 1}$, an asymptotic expansion for the distribution of the least squares estimator of $\theta_0$ is obtained.