Estimating Functions and Equations : An Essay on Historical Developments with Applications to Econometrics

The idea of using estimating functions goes a long way back, at least to Karl Pearson's introduction to the method of moment in 1894. It is now a very active area of research in the statistics literature. One aim of this chapter is to provide an account of the developments relating to the theory of estimating functions. Starting from the simple case of single parameter under independent set up, we cover the multi-parameter, presence of nuisance parameters and dependent data cases. Applications of the estimating function technique to econometrics is still at its infancy. However, we illustrate how this estimation approach could be used in various time series models, such as random coefficient, threshold, bilinear, autoregressive conditional heteroscedasticity models, also in spatial, longitudinal data and median regression analyses. The chapter is concluded with some remarks on the place of estimating function in the history of the statistical estimation techniques