Standard Error for Parameter of Nonlinear Regression

Definition

Suppose a Nonlinear Regression Model $Y_i=f({\mathbf{X}}_i,\mathbf{\theta })+{ϵ}_i,i=1,2,\dots ,n$ The standard error for parameter of nonlinear regression ${\theta }_j$ is calculated as $SE({\hat{\theta }}_j)=\sqrt{c_j}s$ where $c_j=\mathrm{diag}[({\hat{\mathbf{J}}}^{⊺}\hat{\mathbf{J}}{)}^{-1}{]}_j$, $s^2=\frac{{\sum }_{i=1}^n(Y_i-f({\mathbf{X}}_i,\hat{\mathbf{\theta }}){)}^2}{n-p}$, and $\hat{\mathbf{J}}=\left(\frac{\partial f({\mathbf{X}}_i,\mathbf{\theta })}{\partial {\theta }_j}\right){|}_{\mathbf{\theta }=\hat{\mathbf{\theta }}}$is the Jacobian Matrix of $f$.