Consistent Pseudo-Maximum Likelihood Estimators and Groups of Transformations
在变换模型中，当误差独立同分布且与解释变量独立时，伪最大似然估计通常不一致。本文通过将初始模型嵌套到参数更多的识别增强模型中，推导出参数适当函数的一致伪最大似然估计量，并举例说明其在非线性方程组、条件异方差模型、随机波动或空间交互模型中的用途。
In a transformation model , where the errors are i.i.d. and independent of the explanatory variables , the parameters can be estimated by a pseudo‐maximum likelihood (PML) method, that is, by using a misspecified distribution of the errors, but the PML estimator of is in general not consistent. We explain in this paper how to nest the initial model in an identified augmented model with more parameters in order to derive consistent PML estimators of appropriate functions of parameter . The usefulness of the consistency result is illustrated by examples of systems of nonlinear equations, conditionally heteroscedastic models, stochastic volatility, or models with spatial interactions.