Parametric and Non‐parametric Encompassing Procedures*
研究一般回归模型中涵盖统计量的渐近行为，提出四种情况下（参数对参数、非参数对非参数、参数对非参数、非参数对参数）的检验方法，并处理了非参数估计中窗宽自动选择的问题。
Abstract We study the asymptotic behaviour of encompassing statistics in general regression models. The theory for testing one parametric model against another parametric model is now well known, but the comparison of two non‐parametric models, or ‘crossed’ situations where a parametric model is tested against a non‐parametric one, has not been treated previously. The encompassing test statistics for the four cases presented here are based on an appropriately normalized difference between an estimator of parameters (eventually functional), and its pseudo‐true value under . The specification tests for non‐parametrically estimated models have meaning only when the smoothing parameter is not arbitrarily chosen, and so the window widths are calculated by an automatic empirical method (cross‐validation). As the window width determination is part of the estimation procedure, the pseudo‐true window width, associated with the pseudo‐true value, is defined.