Nonlinear regression models with increasing numbers of unknown parameters

An approach for determining least squares estimators and covariance matrix elements is proposed to construct a confidence interval for the unknown function in nonlinear regression models with an increasing number of unknown parameters. The number of unknown parameters depend on the number of observations and a least square estimator is constructed by the iterative procedure. The minimum number of iteration steps are found, which is helpful in finding the asymptotic normality. A random variable is derived that is found to be the normal equation for the least squares estimator. The least squares estimators are used to construct an asymptotic confidence interval for the unknown function in nonlinear regression model.