DIRECTIONALLY DIFFERENTIABLE ECONOMETRIC MODELS
研究了方向可微拟似然函数下拟极大似然估计量的极限分布，将其表示为方向索引的高斯随机过程泛函，并重新定义了拟似然比、Wald和拉格朗日乘子检验统计量，使它们在模型框架下具有规则的零假设极限行为。
The current article examines the limit distribution of the quasi-maximum likelihood estimator obtained from a directionally differentiable quasi-likelihood function and represents its limit distribution as a functional of a Gaussian stochastic process indexed by direction. In this way, the standard analysis that assumes a differentiable quasi-likelihood function is treated as a special case of our analysis. We also examine and redefine the standard quasi-likelihood ratio, Wald, and Lagrange multiplier test statistics so that their null limit behaviors are regular under our model framework.