STATISTICAL INFERENCE WITH SIMULATED LIKELIHOOD FUNCTIONS
研究了在模拟估计下经典检验统计量（似然比、得分和Wald统计量）的渐近性质，发现模拟得分向量可能导致非中心卡方分布，并通过蒙特卡洛模拟比较了有限样本表现。
This paper considers classical test statistics, namely, the likelihood ratio, efficient score, and Wald statistics, for econometric models under simulation estimation. The simulated likelihood ratio, simulated efficient score, and simulated Wald test statistics are shown to be asymptotically equivalent. Because the simulated score vector can be asymptotically biased, limiting distributions of these simulated statistics can be asymptotically noncentral χ2 distributed. This paper studies inference issues with various simulated test statistics. Monte Carlo results are also provided to compare and demonstrate finite sample properties of simulated test statistics.