Asymptotic Results for Generalized Wald Tests
研究了基于广义逆加权矩阵的二次型在样本量趋于无穷时收敛到卡方分布的条件，给出了充要条件，对Hausman设定检验和拟合优度检验等广义Wald检验的渐近显著性水平和局部功效性质有重要意义。
This paper presents conditions under which a quadratic form based on a g- inverted weighting matrix converges to a chi-square distribution as the sample size goes to infinity. Subject to fairly weak underlying conditions, a necessary and sufficient condition is given for this result. The result is of interest because it is needed to establish asymptotic significance levels and local power properties of generalized Wald tests (i.e., Wald tests with singular limiting covariance matrices). Included in this class of tests are Hausman specification tests and various goodness-of-fit tests, among others. The necessary and sufficient condition is relevant to procedures currently in the econometrics literature because it illustrates that some results stated in the literature only hold under more restrictive assumptions than those given.