Testing a Nonlinear Regression Specification: A Nonregular Case

Abstract A statistical test of whether an additive nonlinear term in the response function should be omitted from a nonlinear regression specification is considered. The regularity conditions used to obtain the asymptotic distributions of the customary test statistics are violated when the null hypothesis of omission is true. Moreover, standard iterative algorithms are likely to perform poorly when the data support the null hypothesis. Methods designed to circumvent these mathematical and computational difficulties are described and illustrated.

摘要：考虑了一种关于在非线性回归模型设定中是否应省略响应函数中的加性非线性项的统计检验。当省略的零假设为真时，用于获得常规检验统计量渐近分布的正则条件被违反。此外，当数据支持零假设时，标准迭代算法可能表现不佳。描述并举例说明了旨在规避这些数学和计算困难的方法。