Mathematical Sciences: Strong Approximations of the Distributions of Estimators in Linear Stochastic Models

本课题的研究目的是建立线性随机模型中参数估计量分布的适当近似。通过近似，还包括Berry.Essen界和渐近展开式。将使用的方法将不同于通常的特征函数方法，并且将在所有Borel子集上一致地给出近似，这也是本项目的目标之一。一些具体的统计模型将被详细考虑，包括非线性回归、自回归、因变量滞后的回归。除了考虑最小二乘估计外，还将考虑这些模型中的稳健版本的估计器。

The research for this project is directed at establishing suitable approximations to the distributions of estimators of parameters in linear stochastic models. By approximations, Berry.Essen bounds and asymptotic expansions are also included. The method that will be used will be different from the usual method of characteristic functions and will also give approximations uniformly over all Borel subsets, which is also one of the aims of the project. Some specific statistical models that will be considered in detail include nonlinear regression, autoregression, regression with lagged dependent variables. Robust versions of the estimators in these models will be considered in addition to the least squares estimators.