Gauss-Newton Method for Nonlinear Regression Model with an Increasing Number of Unknown Parameters

In this paper, nonlinear regression models with an increasing number of unknown parameters are considered.The specificity of these models is that the variances of random errors are unknown and different.At each point of observation there is no more than one response which does not allow to estimate variances.Using Gauss-Newton approach, the iterative process for finding the least square estimates has been created.The conditions for convergence of the iterative process are found.It is shown that under some conditions the deviation vector of unknown parameters has Gaussian distribution, which allows to create a confidence band for unknown functions in nonlinear regression models.