Some Non-Nested Hypothesis Tests and the Relations Among Them
讨论了几种检验非线性多元回归模型有效性的统计方法，证明不同检验在特定条件下渐近等价，并通过抽样实验展示小样本下它们的行为差异。
In this paper we discuss several statistical techniques which may be used to test the validity of a possibly non-linear and multivariate regression model, using the information provided by estimating one or more alternative models on the same set of data. We first exposit, from a different perspective, the tests proposed by us in Davidson and MacKinnon (1981a), and discuss modified versions of these tests and extensions of them to the multivariate case. We then prove that all these tests, and also the tests previously proposed by Pesaran (1974) and Pesaran and Deaton (1978), based on the work of Cox (1961, 1962), are asymptotically equivalent under certain conditions. Finally, we present the results of a sampling experiment which shows that different tests can behave quite differently in small samples.