Hypothesis testing of 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 null hypothesis $H_0:{\theta }_j={\theta }_{j,0}$ can be tested with the test statistic $t_j=\frac{{\hat{\theta }}_j-{\theta }_{j,0}}{SE({\hat{\theta }}_j)}\sim t(n-p)$ where $SE({\hat{\theta }}_j)$ is the Standard Error for Parameter of Nonlinear Regression ${\theta }_j$, and $p-1$ is the number of explanatory variables.