Denote the vector of n responses by Y = (Y1Y2, ..., Yn)‘. A nonlinear model is defined by the following properties:
The Yi are independent and identically distributed with an exponential family distribution.
The expected value of each Yi given a vector of predictor values xi is a nonlinear function of parameters, θ. Denote this function as follows:
Each Yi is expressed as follows:
The vector of errors, ε = (ε1ε2, ..., εn)‘ has mean 0 and covariance matrix σ2I, where I is the n x n identity matrix.
Denote the matrix of first partial derivatives of the function f with respect to the parameters θ by X. Under general conditions, the least squares estimator of θ is asymptotically unbiased, with asymptotic covariance matrix given as follows:

Help created on 9/19/2017