The stochastic difference between econometric statistics.

*(English)*Zbl 0722.62067The concept of stochastic difference (the order in probability of the difference) between two statistics is used to compare alternative estimators which are equally efficient asymptotically. A method for computing stochastic difference is derived and used to compare a target estimator with an estimator defined by the k th iteration of an optimization algorithm.

Several optimal algorithms are considered. Relationships between stochastic difference and higher order efficiency comparisons are explored, and a justification for estimators obtained via a search of the objective function is provided. The results are general in nature but are applied to maximum likelihood, nonlinear least squares, and three-stage least-squares estimation of simultaneous equation models as well as to iterative procedures used to obtain these estimators.

Several optimal algorithms are considered. Relationships between stochastic difference and higher order efficiency comparisons are explored, and a justification for estimators obtained via a search of the objective function is provided. The results are general in nature but are applied to maximum likelihood, nonlinear least squares, and three-stage least-squares estimation of simultaneous equation models as well as to iterative procedures used to obtain these estimators.

##### MSC:

62P20 | Applications of statistics to economics |

62F12 | Asymptotic properties of parametric estimators |