An Introduction to Best Empirical Models when the Parameter Space is Infinite Dimensional*
扩展了Ploberger和Phillips（2003）的结论，将有限维参数空间下经验模型与真实模型接近程度的界推广到无限维情形，讨论了无限维模型选择的技术困难及其对预测的含义，并应用于无限阶向量自回归模型。
Abstract Ploberger and Phillips ( Econometrica , Vol. 71, pp. 627–673, 2003) proved a result that provides a bound on how close a fitted empirical model can get to the true model when the model is represented by a parameterized probability measure on a finite dimensional parameter space. The present note extends that result to cases where the parameter space is infinite dimensional. The results have implications for model choice in infinite dimensional problems and highlight some of the difficulties, including technical difficulties, presented by models of infinite dimension. Some implications for forecasting are considered and some applications are given, including the empirically relevant case of vector autoregression (VAR) models of infinite order.