Nonlinear least squares and maximum likelihood estimation of a heteroscedastic regression model

This paper is concerned with the linear regression model in which the variance of the dependent variable is proportional to an unknown power of its expectation. A nonlinear least squares estimator for the model is derived and shown to be strongly consistent and asymptotically normally distributed. Under the assumption of normality, an iterative procedure is suggested to obtain maximum likelihood estimates of the model. The procedure is then shown to converge.